Rewrite each of the following statements in the if-then form. Then write the converse, inverse, and contrapositive of your implication. For each result in parts (a) and (c) give the truth value for the implication and the truth values for its converse, inverse, and contrapositive. [In part (a) “divisibility” requires a remainder of 0.]
a) [The universe comprises all positive integers.] Divisibility by 21 is a sufficient condition for divisibility by 7.
b) [The universe comprises all snakes presently slithering about the jungles of Asia.]
Being a cobra is a sufficient condition for a snake to be dangerous.
c) [The universe consists of all complex numbers.]
For every complex number z, z being real is necessary for z2 to be real.
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