Write the statements formally using quantifiers and variables. Make them conditional.

Question

Write the statements formally using quantifiers and variables. Make them conditional.

1. a) A sufficient condition for an integer to be divisible by 8 is that it be divisible by 16.
2. b) If a product of two real numbers is zero, then one of the numbers must be zero.
3. c) The square of any rational number is rational.

Answer 1

Vx mean FOR ALL X in the set

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a) If The number is divisible by 16 then the number is divisible by 8

(x mod 16 = 0) --> (x mod 8)=0

b) If XY=0 then x=0 or y=0 for any real numbers x and y

Vx in R, (xy=0) --> (x=0) v (y=0)

c) is X is rational then X^2 is rational

(Vx in Q) X^2 in Q