Question

Given: p: x is prime. q: x is even. What is the truth value of p^q when x is replaced by 2? p^q is sometimes true p^q is true p^q is false Not enough information is provided

Answer 1

Answer: true

Step-by-step explanation

p = 2 is prime = true

q = 2 is even = true

p ^ q = true ^ true = true

Both parts of p ^ q need to be true for the overall statement p ^ q to be true; otherwise p ^ q is false.

Here's what the truth table looks like

`\begin{array}c \cline{1-3}\text{p} & \text{q} & \text{p} \wedge \text{q}\\\cline{1-3}\text{T} & \text{T} & \text{T}\\\cline{1-3}\text{T} & \text{F} & \text{F}\\\cline{1-3}\text{F} & \text{T} & \text{F}\\\cline{1-3}\text{F} & \text{F} & \text{F}\\\cline{1-3}\end{array}`

T = true

F = false

For more information, search out "logic conjunction".