Question

Select the relations that are functions.

A. {(a, 1), (b, 1), (c, 1)}
B. {(a, a), (a, b), (a, c)}
C. {(1, a), (2, a), (3, a)}
D. {(a, a), (b, b), (c, c)}

Answer 1

The correct options are A, B and C.

Explanation:

A relation is called a function if there exist a unique output for each input. In other words there exist a unique value of y for each value of x.

In relation A,

{(a, 1), (b, 1), (c, 1)}

In the above relation, for each value of x, we have a unique value of y, therefore this relation is a function and option A is correct.

In relation B,

{(a, a), (a, b), (a, c)}

In the above relation, for each value of x, we have same value of y, therefore this relation is not a function and option B is incorrect.

In relation C,

{(1, a), (2, a), (3, a)}

In the above relation, for each value of x, we have a unique value of y, therefore this relation is a function and option C is correct.

In relation D,

{(a, a), (b, b), (c, c)}

In the above relation, for each value of x, we have a unique value of y, therefore this relation is a function and option D is correct.

Answer 2

functions are, for every input there is 1 output
(x,y)
x is input
basically, x must never repeat with a different y
but y can repeat with different x's
(3,4) and (3,5) is not a function
but (3,4) and (5,4) is


look at them
I will assume a and b and c are different
A. a, b, and c are different so this is a function
B. A repeats with a,b, and c,not a function
C. 1 and 2 and 3 are different numbers so this is a function
D. a b and c don't repeat, this is a function

answer is A, C and D are functions