Solution for Section 2.1 Question 1

1. The truth set for the predicate P(x) is all the values of x in the domain which make the predicate true.

The truth set for P(x) is {10, 20, 30, 40, 50, 60, 70, 80, 90}.

The truth set for S(x) is {5, 10, 15, 20, 25, ..., 85, 90, 95}.

Since every value which is in the truth set for P(x) is also in the truth set for S(x) we can say that "For all x in the domain, if P(x) is true then S(x) is also true." Symbolically this can be represented as " x inred.jpg (595 bytes){1,2, ..., 99}, P(x) impliesred.jpg (864 bytes)S(x).

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