Find counterexamples to show that the statements in 9-12 are false. Forall x R,

Question

Find counterexamples to show that the statements in 9-12 are false. Forall x R, x > 1/x. Forall_a Z, (a - 1)/a is not an integer. Forall positive integers m and n, m middot n greaterthanorequalto m + n. Forall real numbers x and y, y Squareroot x + y = Squareroot x + Squareroot y. Consider the following statement: Forall basketball players x, x is tall. Which of the following are equivalent ways of expressing this statement? a. Every basketball player is tall. b. Among all the basketball players, some are tall. c. Some of all the tall people are basketball players. d. Anyone who is tall is a basketball player. e. All people who are basketball players are tall. f. Anyone who is a basketball player is a tall person.

Explanation / Answer

9. x= 1/2, 1/x =2 we know 2> 1/2 , so the statement is false

10. If a=1 , (a-1)/a = (1-1)/1 = 0 which is an integer

11. m=1, n=2, mn= 1*2=2 , m+n= 1+2=3 .... here 2<3 so the statement proves to be wrong

12. x= 4, y= 9, square root of (x+y)= square root of (4+9)= square root of 13

square root of 4 +   square root of 9= 2+3 =5 so they are not equal

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