13. With apologies to Sidney Harris for trading on his terrific cartoon (shown b

Question

13. With apologies to Sidney Harris for trading on his terrific cartoon (shown below). I'd like to play a little with the dog's statement. Consider the assertions made by the dog: A- "All cats have four legs" B:- have four legs" C:"I am a cat" (Are these assertions statements or predicates? Explain.) The dog's statement is of the form "If A and B, then C" a. Construct a truth table for the statement "If A and B, then C 14. (a). Let a, b E R, with a# O. Show that f: R R, given by f(x) = ax + b is a one-to-one correspondence. (What happens if a-o?) (b). Show that for all positive real numbers k.f-) (-o, k). given by one-to one correspondence. kx x+k2 (c). Show that there exists no positive real number k for which f: R R, given by f(x) = Vkx2 + 5 is a one-to-one correspondence.

Explanation / Answer

17. 44 is divided by 8 : Quotient = 5, Remainder = 4

b. -123 is divided by 19 : Quotient = -6, Remainder = -9

c. 0 is divided by 17: Quotient = 0, Remainder = 0

d. 1234567 is divided by 101 : Quotient = 12223, Remainder = 44

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