True or False ( If a statement is FALSE, give an example that shows it is false.

ID: 3167415 • Letter: T

Question

True or False ( If a statement is FALSE, give an example that shows it is false.)

a) Suppose a,b,c are integers and a does not = 0. If ab=ac(mod 8), then b=c.

b) Let a,b,c be Integers. If a is congruent to b(mod 4) and b is congruent to c(mod 4) then a is congruent to c(mod 2).

c) Let a,b,c be Integers. If a is congruent to b(mod 2) and b is congruent to c(mod 4) then a is congruent to c(mod 2).

d) Let a,b,c be Integers. If a is congruent to b(mod 2) and b is congruent to c(mod 2) then a is congruent to c(mod 4).

1) false , as if a=2 , b= 9 then 18 =2c(mod8) => c = 1 . Hence b is not same as c.

2) false . Let a= 18 then b is 2 . And c is 2 .

Thus a is not c(mod 2 )

3) true . There is not counterexample as the statement is true .

4) false . Take a=18 then b is 0 and c is also 0 but 18 is nit 0mod4 . It is 2 mod4

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