Explain a contrapositive equivalency. How do we know that the contrapositive of a statement, is equivalent to the statement it- self? Show your work.

Answer the following questions in full sentences, with all your work included, to the best of your ability. Make sure the answers are your own.

In your own words, explain a contrapositive equivalency. How do we know that the contrapositive of a statement, is equivalent to the statement it- self? Show your work.

What is the difference between a sufficient condition and a necessary con- dition? Can we represent each conditional using the formal logic we have learned? How? Provide an example of a necessary condition, versus a sufficient condition.

Construct a detailed truth table for the following sentence: (((P ∨Q)∧¬P)→Q)

What is an example of a sentence (formula using our logical tools) that is always true. NB sentences that are always true are known as tautologies.

Suppose S is always true. Given that S is a tautology, write a detailed truth table for the sentence ((S ∧ R) → T ). Can you think of another sentence that yields the exact same truth table as the one above? Explain.