Discrete Math Practice Questions with Correct
Answers
Juan is a math major but not a computer science major. (m = "Juan is a math
major;" c = "Juan is a computer science major.")
m ⋀ ~c
Write the statements in symbolic form using the symbols ~, ⋁, and ⋀ and the indicated
letters to represent component statements.
Let h = "John is healthy," w = "John is wealthy," and s = "John is wise."
John is healthy and wealthy but not wise.
(h ⋀ w) ⋀ ~s
Write the statements in symbolic form using the symbols ~, ⋁, and ⋀ and the indicated
letters to represent component statements.
Let h = "John is healthy," w = "John is wealthy," and s = "John is wise."
John is not wealthy, but he is healthy and wise.
~w ⋀ (h ⋀ s)
Write the statements in symbolic form using the symbols ~, ⋁, and ⋀ and the indicated
letters to represent component statements.
Let h = "John is healthy," w = "John is wealthy," and s = "John is wise."
John is neither healthy, wealthy, nor wise.
~w ⋀ ~h ⋀ ~s
,Write the statements in symbolic form using the symbols ~, ⋁, and ⋀ and the indicated
letters to represent component statements.
Let h = "John is healthy," w = "John is wealthy," and s = "John is wise."
John is wealthy, but he is not both healthy and wise.
w ⋀ ~(h ⋁ s)
Write the statement in symbolic form using the symbols ~, ∨, and ∧ and the indicated
letters to represent component statements.
Let p = "x > 6," q = "x = 6," and r = "11 > x.
x≥6
p∨q
Write the statement in symbolic form using the symbols ~, ∨, and ∧ and the indicated
letters to represent component statements.
Let p = "x > 6," q = "x = 6," and r = "11 > x.
11 > x > 6
r∧p
Write the statement in symbolic form using the symbols ~, ∨, and ∧ and the indicated
letters to represent component statements.
Let p = "x > 6," q = "x = 6," and r = "11 > x.
11 > x ≥ 6
r ∧ (p ∨ q)
,Use De Morgan's laws to write the negation for the statement.
The train is late or my watch is fast.
The train is not late and my watch is not fast.
Assume x is a particular real number and use De Morgan's laws to write the negation
for the statement.
−4 < x < 3
−4 ≥ x or x ≥ 3
Assume x is a particular real number and use De Morgan's laws to write the negation
for the statement.
x ≤ −4 or x > 4
x > −4 and x ≤ 4
Determine whether the statements in A and B are logically equivalent.
Statement A: Bob is both a math and computer science major and Ann is a math major,
but Ann is not both a math and computer science major.
Statement B: It is not the case that both Bob and Ann are both math and computer
science majors, but it is the case that Ann is a math major and Bob is both a math and
computer science major.
Let b be "Bob is a double math and computer science major," m be "Ann is a math
major," and a be "Ann is a double math and computer science major." Create a truth
table for the two statements.
, Write the statements in symbolic form using the symbols ~, ∨, and ∧ and the indicated
letters to represent component statements.
Statement A
(b ∧ m) ∧ ~a
Determine whether the statements in A and B are logically equivalent.
Statement A: Bob is both a math and computer science major and Ann is a math major,
but Ann is not both a math and computer science major.
Statement B: It is not the case that both Bob and Ann are both math and computer
science majors, but it is the case that Ann is a math major and Bob is both a math and
computer science major.
Let b be "Bob is a double math and computer science major," m be "Ann is a math
major," and a be "Ann is a double math and computer science major." Create a truth
table for the two statements.
Write the statements in symbolic form using the symbols ~, ∨, and ∧ and the indicated
letters to represent component statements.
Statement B
~ (b ∧ a) ∧ (m ∧ b)
Rewrite the statement in if-then form.
Fix my ceiling or I won't pay my rent.
If you don't fix my ceiling, then I won't pay my rent.
Answers
Juan is a math major but not a computer science major. (m = "Juan is a math
major;" c = "Juan is a computer science major.")
m ⋀ ~c
Write the statements in symbolic form using the symbols ~, ⋁, and ⋀ and the indicated
letters to represent component statements.
Let h = "John is healthy," w = "John is wealthy," and s = "John is wise."
John is healthy and wealthy but not wise.
(h ⋀ w) ⋀ ~s
Write the statements in symbolic form using the symbols ~, ⋁, and ⋀ and the indicated
letters to represent component statements.
Let h = "John is healthy," w = "John is wealthy," and s = "John is wise."
John is not wealthy, but he is healthy and wise.
~w ⋀ (h ⋀ s)
Write the statements in symbolic form using the symbols ~, ⋁, and ⋀ and the indicated
letters to represent component statements.
Let h = "John is healthy," w = "John is wealthy," and s = "John is wise."
John is neither healthy, wealthy, nor wise.
~w ⋀ ~h ⋀ ~s
,Write the statements in symbolic form using the symbols ~, ⋁, and ⋀ and the indicated
letters to represent component statements.
Let h = "John is healthy," w = "John is wealthy," and s = "John is wise."
John is wealthy, but he is not both healthy and wise.
w ⋀ ~(h ⋁ s)
Write the statement in symbolic form using the symbols ~, ∨, and ∧ and the indicated
letters to represent component statements.
Let p = "x > 6," q = "x = 6," and r = "11 > x.
x≥6
p∨q
Write the statement in symbolic form using the symbols ~, ∨, and ∧ and the indicated
letters to represent component statements.
Let p = "x > 6," q = "x = 6," and r = "11 > x.
11 > x > 6
r∧p
Write the statement in symbolic form using the symbols ~, ∨, and ∧ and the indicated
letters to represent component statements.
Let p = "x > 6," q = "x = 6," and r = "11 > x.
11 > x ≥ 6
r ∧ (p ∨ q)
,Use De Morgan's laws to write the negation for the statement.
The train is late or my watch is fast.
The train is not late and my watch is not fast.
Assume x is a particular real number and use De Morgan's laws to write the negation
for the statement.
−4 < x < 3
−4 ≥ x or x ≥ 3
Assume x is a particular real number and use De Morgan's laws to write the negation
for the statement.
x ≤ −4 or x > 4
x > −4 and x ≤ 4
Determine whether the statements in A and B are logically equivalent.
Statement A: Bob is both a math and computer science major and Ann is a math major,
but Ann is not both a math and computer science major.
Statement B: It is not the case that both Bob and Ann are both math and computer
science majors, but it is the case that Ann is a math major and Bob is both a math and
computer science major.
Let b be "Bob is a double math and computer science major," m be "Ann is a math
major," and a be "Ann is a double math and computer science major." Create a truth
table for the two statements.
, Write the statements in symbolic form using the symbols ~, ∨, and ∧ and the indicated
letters to represent component statements.
Statement A
(b ∧ m) ∧ ~a
Determine whether the statements in A and B are logically equivalent.
Statement A: Bob is both a math and computer science major and Ann is a math major,
but Ann is not both a math and computer science major.
Statement B: It is not the case that both Bob and Ann are both math and computer
science majors, but it is the case that Ann is a math major and Bob is both a math and
computer science major.
Let b be "Bob is a double math and computer science major," m be "Ann is a math
major," and a be "Ann is a double math and computer science major." Create a truth
table for the two statements.
Write the statements in symbolic form using the symbols ~, ∨, and ∧ and the indicated
letters to represent component statements.
Statement B
~ (b ∧ a) ∧ (m ∧ b)
Rewrite the statement in if-then form.
Fix my ceiling or I won't pay my rent.
If you don't fix my ceiling, then I won't pay my rent.
