Question

Use equivalences to prove the following (do not use truth tables) (P→Q1)∨(P→Q2)≡P→(Q1∨Q2) Hint: Start with the left-hand-side ((P→Q1)∨(P→Q2)). Apply a known equivalence to obtain an equivalent formula. Write down the equivalent formula and the equivalence used. Repeat this process until you obtain the right-hand side (P→(Q1∨Q2)).

Does the following hold? If it does, then prove it using equivalences (similar to the previous question). If it does not hold then write a truth table that shows the two formulas are not equivalent.(P→Q1)∧(P→Q2)≡P→(Q1∧Q2)

Answer 1