Question

If M = {-2,-1,1,2,4}, then find the relation $\text{P : M}\to \text{M}$ such that the first component is half the second component.

• A. {(-1,-2),(1,2),(2,4)}
• B. {(-1,-2),(1,4),(2,4)}
• C. {(-1,2),(1,2),(2,4)}
• D. {(1,-2),(-1,2),(2,4)}

Answer 1

The correct option is A {(-1,-2),(1,2),(2,4)}

Given, M = {-2,-1,1,2,4}.
$\because$ -1 is half of -2
-0.5 is half of -1
1 is half of 2
0.5 is half of 1
2 is half of 4
$\therefore$ The possible ordered pairs are {(-1,-2), (-0.5, -1), (0.5, 1), (1,2),(2,4)}. But -0.5 and 0.5 are not the elements of 'M'.

Hence P = {(-1,-2), (1,2),(2,4)}