Q.Using truth tables, prove the following logical equivalence: $(p \land q) \to r \equiv p \to (q \to r)$

Construct a joint truth table over p, q, r (8 rows) for both sides.

p=T,q=T,r=T: LHS (p∧q)→r = T→T=T. RHS q→r=T→T=T, p→(q→r)=T→T=T. Match.

p=T,q=T,r=F: LHS T→F=F. RHS q→r=T→F=F, p→(q→r)=T→F=F. Match.

p=T,q=F,r=T: LHS p∧q=F, F→T=T. RHS q→r=F→T=T, p→T=T. Match.

p=T,q=F,r=F: LHS p∧q=F, F→F=T. RHS q→r=F→F=T, p→T=T. Match.

p=F,q=T,r=T: LHS p∧q=F, F→T=T. RHS q→r=T→T=T, p→T: since p=F, F→anything=T. Match.

p=F,q=T,r=F: LHS p∧q=F, F→F=T. RHS q→r=T→F=F, p→(q→r)=F→F=T (p=F makes it T). Match. …

When p is F, both sides collapse to T automatically (false antecedent) — students sometimes still try to evaluate q→r there …