Question

HELP!! TRUTH TABLE

I would really appreciate it, if someone could walk me through how they did it! Thanks.

Answer 1

p ∧ q (i.e. "p and q") is true only if both p and q are true. This is the case for the first two rows, but not the third.

Similarly, (p ∧ q) ∧ r is true only if both p ∧ q and r are true. We know when p ∧ q is true, so (p ∧ q) ∧ r is true only when all three of p, q, and r are true. This happens only in the first row.

All other cases are false.

The table should look like this:

`\begin{array}cp&q&r&p\land q&(p\land q)\land r) \\---&---&---&---&--- \\T&T&T&\boxed T&\boxed T\\&&&&\\T&T&F&\boxed T&\boxed F\\&&&&\\T&F&T&\boxed F&\boxed F\end{array}`