NIMCET 2015 — Computer PYQ

Step 1: Simplify the premises $\{q\to s,r\to s\}$

According to the rule of Disjunctive Syllogism or Constructive Dilemma (specifically the property of implication), if two different antecedents lead to the same consequent, their disjunction also leads to that consequent:

Step 2: Combine with the first premise

Now we have two main implications:

1. $p\to (q\vee r)$

2. $(q\vee r)\to s$

Step 3: Apply the Law of Hypothetical Syllogism

The Law of Hypothetical Syllogism (Transitive Property) states that if $A\to B$ and $B\to C$, then $A\to C$.

Using:

• $A=p$

• $B=(q\vee r)$

• $C=s$

Since $p\to (q\vee r)$ and $(q\vee r)\to s$, we can conclude:

Conclusion:

The set of premises $\{p\to q\vee r,q\to s,r\to s\}$ is logically equivalent to $p\to s$.

The correct option is (c).