The compound proposition "p AND (q OR r)" is:a.Tautologyb.Contradictionc.Contingencyd.None of the above

The compound proposition "p AND (q OR r)" is a contingency. This is because the truth value of the proposition depends on the truth values of p, q, and r. It is not always true (a tautology) or always false (a contradiction), but rather its truth value is contingent on the values of the individual propositions.

To determine the nature of the compound proposition "p AND (q OR r)", we need to evaluate its truth values for all possible combinations of truth values for p, q, and r.

Step 1: Evaluate the truth value of q OR r.

• If q is true or r is true, then q OR r is true.
• If both q and r are false, then q OR r is false.

Step 2: Evaluate the truth value of p AND (q OR r).

• If p is true and q OR r is true, then p AND (q OR r) is true.
• If p is false, then p AND (q OR r) is false, regardless of the truth value of q OR r.

Based on these evaluations, we can conclude that the compound proposition "p AND (q OR r)" is a contingency.