| (a) | Let A be the null set. | |
| (i) What is the cardinality of A? | [1] | |
| (ii) What is the cardinality of the power set P(A)? | [1] | |
| (iii) What is the cardinality of the power set P(P(A))? | [1] | |
| (iv) List the elements of the power set
P(P(P(A))).
|
[1] | |
| (b) | Consider the following statement " basketball players x, x is tallWhich of the following are equivalent ways of expressing this statement? |
[2] |
| (i) Every basketball player is tall. | ||
| (ii) Some basketball players are tall. | ||
| (iii) Some of all tall people are basketball players. | ||
| (iv) Anyone who is tall is a basketball player. | ||
| (v) All people who are basketball players are
tall
|
||
| (c) | (i) How many ways can the letters of the word DESIGN be arranged in a row? | [1] |
| (ii) How many ways can the letters of the word
DESIGN be arranged in a row if G and N must remain next to each other as either GN or NG?
|
[2] | |
| (d) | Given the matrices
|
[3] |
| (e) | Calculate the inverse of the function f(x) = 10 - 2x
|
[3] |
| (f) | Prove by induction that n3 - n is divisible by 6 for n ³ 1. | [5] |
,