Relations and Functions
ICSE · Class 11 · Mathematics
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If A = {1, 2} and B = {3, 4}, what is n(A × B)?
Which of the following is the correct definition of a relation R from A to B?
If R = {(1,4),(2,5),(3,6)} from A = {1,2,3} to B = {4,5,6}, what is the range of R?
What is ⌊3.7⌋ (greatest integer function)?
Sample Questions
The Cartesian product A × B is always equal to B × A.
Show answer
False
A × B ≠ B × A in general because ordered pairs care about position. (a,b) ≠ (b,a) unless a = b. They are equal only when A = B or one is empty.
A function f : A → B is a relation where every element of A has exactly one image in B.
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True
A function requires: (1) every element of A must be mapped, (2) each element of A maps to exactly one element of B. This is the defining condition of a function.
For f(x) = |x|, what is f(−5)?
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5
|x| = −x when x < 0. So |−5| = −(−5) = 5. The modulus function always returns a non-negative value.
The range of f(x) = x² from R to R is all real numbers.
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False
f(x) = x² ≥ 0 for all real x. So the range is [0, ∞), not all of R. Negative numbers like −1 are in the codomain but not in the range.
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