For each relation below explain why it is or isnt a function

For each relation below explain why it is or isn’t a function

a) R: all pairs of integers of the form (x² , x)

b) R:{(1,2), (2,3)(3,4)(3,5)(4,6)}

c) R:{(a,b)| a b mod 10}

Solution

a)

(1,1),(1,-1) are both in R

So, 1 maps to both 1 and -1.

HEnce, R is not a function

b)

3 maps to 4 and 5

Hence, R is not a function

c)

Not a function because

(1,11),(1,21) are both in R

SO, 1 maps to 11 and 21 hence not a function