Question

Using truth table , prove that (p^q) ->r =P (q-> r)​

Answer 1

One possibility is truth tables.

Another possibility is:

(1) Left to right: from P→Q and Q→R, you immediately get P→R. You also need one of P↔Q or P↔R; and the only way for both of these to fail if for P,Q,R to be TFT or FTF, but neither of these cases is compatible with both of the conditionals on the left side.

(2) Right to left: You have P→R, and (at least) one of P↔Q or R↔Q. In the case of P↔Q, you get Q→R by substitution (into P→R), and you get P→Q; thus you get the left side. The other case, where you have R↔Q is similar.