RTUComputer ScienceYr 2024 · Sem 42024

Q4Discrete Mathematics Structure

Question

2 marks

Obtain the DNF of the proposition (p → q) ∧ (~p ∧ q).

Answer

The DNF of (p → q) ∧ (~p ∧ q) is (~p ∧ q).

To find the Disjunctive Normal Form (DNF) of $(p \to q) \land (\sim p \land q)$ :

Replace implication: $(\sim p \lor q) \land (\sim p \land q)$
Distribute: $((\sim p \lor q) \land \sim p) \land q$
Using Absorption Law: $(\sim p) \land q$
Final DNF: $(\sim p \land q)$