(a)[1]
Use set notation to state which part of the Venn diagram is shaded.
(b(i))[2]
$\mathcal{E} = \{1,2,3,4,5,6,7,8,9,10,11,12\}$ $A = \{x : x \text{ is a factor of } 12\}$ $B = \{x : x \text{ is a multiple of } 2\}$ $C = \{x : x \text{ is a square number}\}$ Show the following sets on the Venn diagram below.
(b(ii))[1]
Find the value of $n(A \cap B)$.
(b(iii))[1]
Find the value of $n(A \cap (B \cup C)')$.
(b(iv))[1]
In part (b)(i), one subset of the Venn diagram has no members. Use set notation to write this subset.
(c(i))[2]
Write $540$ in prime-factor form.
(c(ii))[2]
p is the smallest possible integer such that $540p$ is a square number. Find $\sqrt{540p}$, giving your answer as the product of its prime factors.