p ∧ T≡ p

To prove the statement "p ∧ T ≡ p" step by step, we can use the laws of logical equivalence.

Step 1: Start with the left-hand side of the equivalence: "p ∧ T".

Step 2: According to the identity law of conjunction, any statement combined with true (T) using conjunction (∧) will result in the original statement. Therefore, "p ∧ T" is equivalent to "p".

Step 3: Now, compare the right-hand side of the equivalence: "p".

Step 4: Since "p" is the same as "p", we can conclude that "p ∧ T" is equivalent to "p".

Therefore, we have proven that "p ∧ T ≡ p" step by step using the laws of logical equivalence.