Question

If statements $p,q,r$ have truth values T, F, T respectively then which of the following statement is true

• A. $(p\to q)\wedge r$
• B. $(p\to q)\vee \sim r$
• C. $(p\wedge q)\vee (q\wedge r)$
• D. $(p\to q)\to r$

Answer 1

The correct option is D $(p\to q)\to r$

A. $(p\to q)\wedge r\equiv (T\to F)\wedge T\equiv F\wedge T\equiv F$
B. $(p\to q)\vee \sim r\equiv (T\to F)\vee F\equiv F\vee F\equiv F$
C. $(p\wedge q)\vee (q\wedge r)\equiv (T\wedge F)\vee (F\wedge T)\equiv F\vee F\equiv F$
D. $(p\to q)\to r\equiv (T\to F)\to T\equiv F\to T\equiv T$