Question 1. Part (I)Give counterexamples to show each of the following is false:

a) for x=1 and y =2 xy=2*1=2, x+y=2+1=3 xy1/x if x=0.5 0.5

ID: 3666037 • Letter: Q

Question

Question 1.

Part (I)Give counterexamples to show each of the following is false:

(a) For all positive integers x and y, xy > x + y

(b) For all real numbers x, x > 1/x

Part(II) Translate the following English sentences into statements of predicate calculus that contain double quantifiers:

(a) Any even integer is equal to twice some other even integer

(b) Some natural number is no bigger than every natural number

Part (III) Refer to the statements in Part (II) and indicate whether each is true or false. Provide your reasoning.

a) for x=1 and y =2

xy=2*1=2, x+y=2+1=3

xy<x+y

hence it shows its wrong.

b)x>1/x

if x=0.5

0.5<1/0.5

0.5<2

again wrong

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