Which of the following statements are true which are false G

Which of the following statements are true, which are false? Give a short justification (c. g. a counterexample) of your answers. for all x belongs to R, for exist y belongs to R, xy = 1 for all x belongs to N, for exist y belongs to N, for exist z belongs to N, xz = y for all x belongs to N, for exist y belongs to N, 2y = x 2y + 1 = x

Solution

a) False

Let, x=0

Then for all y in R

xy=0

hence no such y exists so that:xy=1

b)

True

Choose

x=y,z=1

c)

False

Counter example

Let, x=1

2y=x =1 is not possible for any y in N

2y+1=x=1 means y=0 but y is in N

Hence no such y exists