Discrete Mathematics Unit 1 study
notes correctly solved 2026
Negation - correct answer ✔Let p be a proposition. ¬p is defined as taking on the opposite truth value
assigned to p.
Conjunction - correct answer ✔Let p and q be propositions. p∧q is true whenever p and q are true;
otherwise p∧q ≡ F.
Disjunction - correct answer ✔Let p and q be propositions. p∨q is false whenever both p and q are
false, but true otherwise.
Direct conditional - correct answer ✔Let p and q be propositions. p→q is the direct conditional
statement such that if p ≡ T and q ≡ F, then p→q ≡ F; otherwise, p→q ≡ T.
Converse - correct answer ✔The conditional statement q→p.
Inverse - correct answer ✔The conditional statement ¬p→¬q.
Contrapositive - correct answer ✔The conditional statement ¬q→¬p.
Exclusive-or - correct answer ✔Let p and q be propositions. p⊕q is true whenever exactly one
proposition is true. Otherwise, p⊕q ≡ F, meaning p and q have exactly the same true value.
De Morgan's Laws - correct answer ✔¬(p∧q)≡¬p∨¬q
¬(p∨q)≡¬p∧¬q
, Identity Laws - correct answer ✔p∧T≡p
p∨F≡p
Domination Laws - correct answer ✔p∨T≡T
p∧F≡F
Idempotent Laws - correct answer ✔p∨p≡p
p∧p≡p
Double Negation Law - correct answer ✔¬(¬p)≡p
Commutative Laws - correct answer ✔p∨q≡q∨p
p∧q≡q∧p
Associative Laws - correct answer ✔(p∨q)∨r≡p∨(q∨r)
(p∧q)∧r≡p∧(q∧r)
Distributive Laws - correct answer ✔p∨(q∧r)≡(p∨q)∧(p∨r)
p∧(q∨r)≡(p∧q)∨(p∧r)
Absorption Laws - correct answer ✔p∨(p∧q)≡p
p∧(p∨q)≡p
Negation Laws - correct answer ✔p∨¬p≡T
p∧¬p≡F
notes correctly solved 2026
Negation - correct answer ✔Let p be a proposition. ¬p is defined as taking on the opposite truth value
assigned to p.
Conjunction - correct answer ✔Let p and q be propositions. p∧q is true whenever p and q are true;
otherwise p∧q ≡ F.
Disjunction - correct answer ✔Let p and q be propositions. p∨q is false whenever both p and q are
false, but true otherwise.
Direct conditional - correct answer ✔Let p and q be propositions. p→q is the direct conditional
statement such that if p ≡ T and q ≡ F, then p→q ≡ F; otherwise, p→q ≡ T.
Converse - correct answer ✔The conditional statement q→p.
Inverse - correct answer ✔The conditional statement ¬p→¬q.
Contrapositive - correct answer ✔The conditional statement ¬q→¬p.
Exclusive-or - correct answer ✔Let p and q be propositions. p⊕q is true whenever exactly one
proposition is true. Otherwise, p⊕q ≡ F, meaning p and q have exactly the same true value.
De Morgan's Laws - correct answer ✔¬(p∧q)≡¬p∨¬q
¬(p∨q)≡¬p∧¬q
, Identity Laws - correct answer ✔p∧T≡p
p∨F≡p
Domination Laws - correct answer ✔p∨T≡T
p∧F≡F
Idempotent Laws - correct answer ✔p∨p≡p
p∧p≡p
Double Negation Law - correct answer ✔¬(¬p)≡p
Commutative Laws - correct answer ✔p∨q≡q∨p
p∧q≡q∧p
Associative Laws - correct answer ✔(p∨q)∨r≡p∨(q∨r)
(p∧q)∧r≡p∧(q∧r)
Distributive Laws - correct answer ✔p∨(q∧r)≡(p∨q)∧(p∨r)
p∧(q∨r)≡(p∧q)∨(p∧r)
Absorption Laws - correct answer ✔p∨(p∧q)≡p
p∧(p∨q)≡p
Negation Laws - correct answer ✔p∨¬p≡T
p∧¬p≡F
