DISCRETE MATH QUESTIONS AND
ANSWERS WITH SOLUTIONS 2024
Statement - ANSWER A statement (proposition) is a sentence that is either true or false, but not both.
Negation - ANSWER A negation of a statement p is the statement "not p" or "it is not the case that p,"
and is denoted by ⌐p. A statement and its negation always have the opposite truth value.
Conjunction - ANSWER The conjunction of two statements p and q is the statement "p and q," and is
denoted by p ᴧ q. The conjunction p ᴧ q is true if both p and q are true and is false otherwise.
Disjunction - ANSWER The disjunction of two statements p and q is the statement "p or q," and is
denoted by p v q. The disjunction p v q is true if either of p and q are true or if both are true.
Conditional - ANSWER A statement of the form "if p, then q" where p and q are statements, is called a
conditional and is denoted by p -> q.
Forms of the conditional statement - ANSWER The conditional, p→ q can be stated in any of the
following ways:
If p, then q
q if p
p implies q
p only if q
p is sufficient for q
q is necessary for p
Tautology - ANSWER A tautology is a statment that is always true no matter what truth values are
assigned to the statements appearing in it.
Fallacy(or Contradiction) - ANSWER A fallacy(or Contradiction) is a statement that is always false.
Contingency - ANSWER A statement that is sometimes false and sometimes true is called a contingency
, De Morgan's Law - ANSWER For statements p and q,
⌐(p ᴧ q) ≡ ⌐p v ⌐q
⌐(p v q) ≡ ⌐p ᴧ ⌐q
Commutative Laws - ANSWER p ᴧ q ≡ q ᴧ p
pvq≡qvp
Associative Laws - ANSWER p ᴧ (q ᴧ r) ≡ (p ᴧ q) ᴧ r
p v (q v r) ≡ (p v q) v r
Distributive Laws - ANSWER p ᴧ (q v r) ≡ (p ᴧ q) v (p ᴧ r)
p v (q ᴧ r) ≡ (p v q) ᴧ (p v r)
Impotent Laws - ANSWER p ᴧ p ≡ p
pvp≡p
Double Negation Law - ANSWER ⌐(⌐p) ≡ p
Negation Laws - ANSWER p ^ ⌐p ≡ F
p v ⌐p ≡ T
Identity Laws - ANSWER p ᴧ T ≡ p
pvF≡p
Universal Bound Laws - ANSWER p ᴧ F ≡ F
pvT≡T
Absorption Laws - ANSWER P ᴧ ( p v q) ≡ p
ANSWERS WITH SOLUTIONS 2024
Statement - ANSWER A statement (proposition) is a sentence that is either true or false, but not both.
Negation - ANSWER A negation of a statement p is the statement "not p" or "it is not the case that p,"
and is denoted by ⌐p. A statement and its negation always have the opposite truth value.
Conjunction - ANSWER The conjunction of two statements p and q is the statement "p and q," and is
denoted by p ᴧ q. The conjunction p ᴧ q is true if both p and q are true and is false otherwise.
Disjunction - ANSWER The disjunction of two statements p and q is the statement "p or q," and is
denoted by p v q. The disjunction p v q is true if either of p and q are true or if both are true.
Conditional - ANSWER A statement of the form "if p, then q" where p and q are statements, is called a
conditional and is denoted by p -> q.
Forms of the conditional statement - ANSWER The conditional, p→ q can be stated in any of the
following ways:
If p, then q
q if p
p implies q
p only if q
p is sufficient for q
q is necessary for p
Tautology - ANSWER A tautology is a statment that is always true no matter what truth values are
assigned to the statements appearing in it.
Fallacy(or Contradiction) - ANSWER A fallacy(or Contradiction) is a statement that is always false.
Contingency - ANSWER A statement that is sometimes false and sometimes true is called a contingency
, De Morgan's Law - ANSWER For statements p and q,
⌐(p ᴧ q) ≡ ⌐p v ⌐q
⌐(p v q) ≡ ⌐p ᴧ ⌐q
Commutative Laws - ANSWER p ᴧ q ≡ q ᴧ p
pvq≡qvp
Associative Laws - ANSWER p ᴧ (q ᴧ r) ≡ (p ᴧ q) ᴧ r
p v (q v r) ≡ (p v q) v r
Distributive Laws - ANSWER p ᴧ (q v r) ≡ (p ᴧ q) v (p ᴧ r)
p v (q ᴧ r) ≡ (p v q) ᴧ (p v r)
Impotent Laws - ANSWER p ᴧ p ≡ p
pvp≡p
Double Negation Law - ANSWER ⌐(⌐p) ≡ p
Negation Laws - ANSWER p ^ ⌐p ≡ F
p v ⌐p ≡ T
Identity Laws - ANSWER p ᴧ T ≡ p
pvF≡p
Universal Bound Laws - ANSWER p ᴧ F ≡ F
pvT≡T
Absorption Laws - ANSWER P ᴧ ( p v q) ≡ p
