Mathematical Logic
EXERCISE 1.1 [PAGES 6 - 8]
Exercise 1.1 | Q 1.01 | Page 6
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
5 + 4 = 13
Solution: It is a statement which is false, hence its truth value is ‘F’.
Exercise 1.1 | Q 1.02 | Page 6
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
x – 3 = 14
Solution: It is an open sentence, hence it is not a statement.
Exercise 1.1 | Q 1.03 | Page 6
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
Close the door.
Solution: It is an imperative sentence, hence it is not a statement.
Exercise 1.1 | Q 1.04 | Page 6
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
Zero is a complex number.
Solution: It is a statement which is true, hence its truth value is ‘T’.
Exercise 1.1 | Q 1.05 | Page 6
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
Please get me breakfast.
Solution: It is an imperative sentence, hence it is not a statement.
Exercise 1.1 | Q 1.06 | Page 6
,State which of the following is the statement. Justify. In case of a statement, state its
truth value.
Congruent triangles are similar.
Solution: It is a statement which is true, hence its truth value is ‘T’.
Exercise 1.1 | Q 1.07 | Page 6
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
x2 = x
Solution: It is an open sentence, hence it is not a statement.
Exercise 1.1 | Q 1.08 | Page 8
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
A quadratic equation cannot have more than two roots.
Solution: It is a statement which is true, hence its truth value is ‘T’.
Exercise 1.1 | Q 1.09 | Page 7
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
Do you like Mathematics?
Solution: It is an interrogative sentence, hence it is not a statement.
Exercise 1.1 | Q 1.1 | Page 7
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
The sunsets in the west
Solution: It is a statement which is true, hence its truth value is ‘T’.
Exercise 1.1 | Q 1.11 | Page 7
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
All real numbers are whole numbers.
Solution: It is a statement which is false, hence its truth value is ‘F’.
,Exercise 1.1 | Q 1.12 | Page 7
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
Can you speak in Marathi?
Solution: It is an interrogative sentence, hence it is not a statement.
Exercise 1.1 | Q 1.13 | Page 7
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
x2 – 6x – 7 = 0, when x = 7
Solution: It is a statement which is true, hence its truth value is ‘T’.
Exercise 1.1 | Q 1.14 | Page 7
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
The sum of cube roots of unity is zero.
Solution: It is a statement which is true, hence its truth value is ‘T’.
Exercise 1.1 | Q 1.15 | Page 7
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
It rains heavily.
Solution: It is an open sentence, hence it is not a statement.
Exercise 1.1 | Q 2.1 | Page 7
Write the following compound statement symbolically.
Nagpur is in Maharashtra and Chennai is in Tamil Nadu.
Solution: Let p: Nagpur is in Maharashtra.
Let q: Chennai is in Tamil Nadu.
Then the symbolic form of the given statement is p∧q.
Exercise 1.1 | Q 2.2 | Page 7
Write the following compound statement symbolically.
Triangle is equilateral or isosceles.
, Solution: Let p: Triangle is equilateral.
Let q: Triangle is isosceles.
Then the symbolic form of the given statement is p∨q.
Exercise 1.1 | Q 2.3 | Page 7
Write the following compound statement symbolically.
The angle is right angle if and only if it is of measure 90°.
Solution: Let p: The angle is right angle.
Let q: It is of measure 90°
Then the symbolic form of the given statement is p↔q.
Exercise 1.1 | Q 2.4 | Page 7
Write the following compound statement symbolically.
Angle is neither acute nor obtuse.
Solution: Let p: Angle is acute.
Let q: Angle is obtuse.
Then the symbolic form of the given statement is ∼p∧∼q.
Exercise 1.1 | Q 2.5 | Page 7
Write the following compound statement symbolically.
If Δ ABC is right-angled at B, then m∠A + m∠C = 90°
Solution: Let p: Δ ABC is right-angled at B.
Let q: m∠A + m∠C = 90°
Then the symbolic form of the given statement is p→q.
Exercise 1.1 | Q 2.6 | Page 7
Write the following compound statement symbolically.
Hima Das wins gold medal if and only if she runs fast.
Solution: Let p: Hima Das wins gold medal
Let q: She runs fast.
Then the symbolic form of the given statement is p↔q.
Exercise 1.1 | Q 2.7 | Page 7
Write the following compound statement symbolically.
EXERCISE 1.1 [PAGES 6 - 8]
Exercise 1.1 | Q 1.01 | Page 6
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
5 + 4 = 13
Solution: It is a statement which is false, hence its truth value is ‘F’.
Exercise 1.1 | Q 1.02 | Page 6
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
x – 3 = 14
Solution: It is an open sentence, hence it is not a statement.
Exercise 1.1 | Q 1.03 | Page 6
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
Close the door.
Solution: It is an imperative sentence, hence it is not a statement.
Exercise 1.1 | Q 1.04 | Page 6
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
Zero is a complex number.
Solution: It is a statement which is true, hence its truth value is ‘T’.
Exercise 1.1 | Q 1.05 | Page 6
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
Please get me breakfast.
Solution: It is an imperative sentence, hence it is not a statement.
Exercise 1.1 | Q 1.06 | Page 6
,State which of the following is the statement. Justify. In case of a statement, state its
truth value.
Congruent triangles are similar.
Solution: It is a statement which is true, hence its truth value is ‘T’.
Exercise 1.1 | Q 1.07 | Page 6
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
x2 = x
Solution: It is an open sentence, hence it is not a statement.
Exercise 1.1 | Q 1.08 | Page 8
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
A quadratic equation cannot have more than two roots.
Solution: It is a statement which is true, hence its truth value is ‘T’.
Exercise 1.1 | Q 1.09 | Page 7
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
Do you like Mathematics?
Solution: It is an interrogative sentence, hence it is not a statement.
Exercise 1.1 | Q 1.1 | Page 7
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
The sunsets in the west
Solution: It is a statement which is true, hence its truth value is ‘T’.
Exercise 1.1 | Q 1.11 | Page 7
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
All real numbers are whole numbers.
Solution: It is a statement which is false, hence its truth value is ‘F’.
,Exercise 1.1 | Q 1.12 | Page 7
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
Can you speak in Marathi?
Solution: It is an interrogative sentence, hence it is not a statement.
Exercise 1.1 | Q 1.13 | Page 7
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
x2 – 6x – 7 = 0, when x = 7
Solution: It is a statement which is true, hence its truth value is ‘T’.
Exercise 1.1 | Q 1.14 | Page 7
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
The sum of cube roots of unity is zero.
Solution: It is a statement which is true, hence its truth value is ‘T’.
Exercise 1.1 | Q 1.15 | Page 7
State which of the following is the statement. Justify. In case of a statement, state its
truth value.
It rains heavily.
Solution: It is an open sentence, hence it is not a statement.
Exercise 1.1 | Q 2.1 | Page 7
Write the following compound statement symbolically.
Nagpur is in Maharashtra and Chennai is in Tamil Nadu.
Solution: Let p: Nagpur is in Maharashtra.
Let q: Chennai is in Tamil Nadu.
Then the symbolic form of the given statement is p∧q.
Exercise 1.1 | Q 2.2 | Page 7
Write the following compound statement symbolically.
Triangle is equilateral or isosceles.
, Solution: Let p: Triangle is equilateral.
Let q: Triangle is isosceles.
Then the symbolic form of the given statement is p∨q.
Exercise 1.1 | Q 2.3 | Page 7
Write the following compound statement symbolically.
The angle is right angle if and only if it is of measure 90°.
Solution: Let p: The angle is right angle.
Let q: It is of measure 90°
Then the symbolic form of the given statement is p↔q.
Exercise 1.1 | Q 2.4 | Page 7
Write the following compound statement symbolically.
Angle is neither acute nor obtuse.
Solution: Let p: Angle is acute.
Let q: Angle is obtuse.
Then the symbolic form of the given statement is ∼p∧∼q.
Exercise 1.1 | Q 2.5 | Page 7
Write the following compound statement symbolically.
If Δ ABC is right-angled at B, then m∠A + m∠C = 90°
Solution: Let p: Δ ABC is right-angled at B.
Let q: m∠A + m∠C = 90°
Then the symbolic form of the given statement is p→q.
Exercise 1.1 | Q 2.6 | Page 7
Write the following compound statement symbolically.
Hima Das wins gold medal if and only if she runs fast.
Solution: Let p: Hima Das wins gold medal
Let q: She runs fast.
Then the symbolic form of the given statement is p↔q.
Exercise 1.1 | Q 2.7 | Page 7
Write the following compound statement symbolically.
