Select the correct answerThe premises (p ∧ q) ∨ r and r → s imply which of the conclusion?Optionsp ∨ sp ∨ rp ∨ qq ∨ r

To solve this problem, we need to understand the logical implications of the premises and then compare them to the options given.

Premise 1: (p ∧ q) ∨ r This means that either both p and q are true, or r is true.

Premise 2: r → s This means that if r is true, then s is also true.

Now, let's look at the options:

Option 1: p ∨ s This means that either p is true, or s is true. This could be true if r is true (because r implies s from Premise 2), or if p is true (from Premise 1). So, this is a possible conclusion.

Option 2: p ∨ r This means that either p is true, or r is true. This could be true if r is true (from Premise 1), or if p is true (also from Premise 1). So, this is also a possible conclusion.

Option 3: p ∨ q This means that either p is true, or q is true. This could only be true if both p and q are true (from Premise 1). But Premise 1 allows for the possibility that only r is true, not p or q. So, this is not a valid conclusion.

Option 4: q ∨ r This means that either q is true, or r is true. This could be true if r is true (from Premise 1), or if both p and q are true (also from Premise 1). So, this is also a possible conclusion.

So, the correct answers are Options 1, 2, and 4: p ∨ s, p ∨ r, and q ∨ r.