Question

question list
question 17
question 18
construct a truth table for the given compound statement: ~(p ∧ q) ∨ ~r
complete the truth table

p	q	r	~r	p ∧ q	~(p ∧ q)	~(p ∧ q) ∨ ~r
t	t	t

question 19
question 20

Explanation:

Step1: Find negation of r

The negation of a true statement is false. When \(r = T\), \(\sim r=F\).

Step2: Find \(p\land q\)

The conjunction \(p\land q\) is true only when both \(p\) and \(q\) are true. Since \(p = T\) and \(q = T\), \(p\land q=T\).

Step3: Find \(\sim(p\land q)\)

The negation of a true statement is false. Since \(p\land q = T\), \(\sim(p\land q)=F\).

Step4: Find \(\sim(p\land q)\lor\sim r\)

The disjunction \(A\lor B\) is false only when both \(A\) and \(B\) are false. Here \(A=\sim(p\land q)=F\) and \(B = \sim r=F\), so \(\sim(p\land q)\lor\sim r=F\).

Answer:

\(p\)	\(q\)	\(r\)	\(\sim r\)	\(p\land q\)	\(\sim(p\land q)\)	\(\sim(p\land q)\lor\sim r\)