Sets and Binary Operations
GCE Further Mathematics

11 Sets and Binary Operations practice questions covering everything you need for GCE.

Drill Sets and Binary Operations

Sample Sets and Binary Operations questions

Q12024· EASY

(a) The universal set U = {x : x is a positive integer, x ≤ 20}. Sets A and B are subsets of U such that A = {x : x is a prime number} and B = {x : x is an odd number}. (i) List the elements of A and…

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Q22019· HARD

(a) A binary operation * is defined on the set of real numbers R by: x * y = x + y + 3xy, for all x, y ∈ R. (i) Show that the operation * is commutative. (ii) Show that the operation * is associative…

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Q32020· EASY

In a class of 40 students, 25 study Mathematics, 20 study Physics, and 10 study both subjects. How many students study neither Mathematics nor Physics?

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Q42019· EASY

If the universal set U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {2, 4, 6, 8}, find A' (the complement of A).

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Q52019· MEDIUM

A binary operation * is defined on the set of real numbers by $a * b = a + b - 2ab$. Find the value of $3 * 2$.

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Q62022· MEDIUM

Given that sets A and B are subsets of the universal set U, which of the following is equivalent to $(A \cup B)'$?

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Q72023· MEDIUM

In a survey of 100 traders in Lagos market, 60 sell rice, 45 sell beans, and some sell both. If 15 traders sell neither rice nor beans, how many traders sell both rice and beans?

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Q82024· HARD

A binary operation * is defined on the set of real numbers by $a * b = \frac{a+b}{1+ab}$, where $ab \neq -1$. If the operation is commutative, find the identity element $e$ such that $a * e = a$.

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Q92019· HARD

A binary operation Δ is defined on the set $S = \{0, 1, 2, 3, 4\}$ by $a \Delta b = (a + b) \mod 5$. Find the inverse of 3 under this operation, given that the identity element is 0.

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Q102020· MEDIUM

A binary operation ⊕ is defined on the set of integers by $p \oplus q = p^2 + q^2 - pq$. Find $2 \oplus 3$.

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Q112024· EASY

If P = {1, 2, 3, 4, 5} and Q = {2, 4, 6, 8}, find P ∩ Q.

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