Question

If p is true, q is false and r is true then the truth value of $\sim p \rightarrow (q \lor r)$ is

• A. F
• B. T
• C. either T or F
• D. cannot be determined

Answer 1

Answer: (B)

T

Answer 2

Given:

• $p = T$
• $q = F$
• $r = T$

Step 1: Compute $\sim p$:

$$\sim p = F$$

Step 2: Compute $q \lor r$:

$$q \lor r = F \lor T = T$$

Step 3: Evaluate the implication:

$$\sim p \rightarrow (q \lor r) = F \rightarrow T$$

Recall that in an implication $A \rightarrow B$, if $A$ is false, the whole statement is true.

Thus, the given expression is T.

$\sim p = F$; $q \lor r = T$; false implies true is always true.