By using laws of algebra of statements show that p or (p and q) is equivalent to p .

Question

I verified the above result using truth tables and got that the LHS is equivalent to the RHS, but I am not able to prove the result using the laws of the algebra of statements. Please guide me.

Answer 1

The first step is to recall that $p\equiv p\wedge T$ by the identity property. Substituting this into the expression gives

$$p\vee(p\wedge q)\equiv (p\wedge T)\vee(p\wedge q)$$.

Next, using the distributive law, we have

$$\equiv p\wedge(T\vee q)$$.

Then, using the identity property twice,

$$\equiv p\wedge T\equiv p$$.