Question

The universal set, &, and sets A, B and C are defined below.

= {2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {2, 4, 6, 8, 10}
B = {2,3,4,5}
C = {6,7,8,9}
Decide whether each statement below is true or false. Show your
working.
a
a) AnB = 0
b) BnC=0
c) 7 E AUB

Answer 1

Part (a)

Claim:
`A \cap B = \varnothing`

Answer: False

Reason: Sets A and B have the numbers 2 and 4 in common.

So it should be
`A \cap B = \{2, 4\}` which means this set is not empty.

Side note: The symbol
`\varnothing` represents the empty set. It's the set with nothing inside it (not even zero).

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Part (b)

Claim:
`B \cap C = \varnothing`

Answer: True

Reason: Sets B and C have nothing in common. Pick any value from B and it won't be found in set C, or vice versa.

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Part (c)

Claim:
`7 \in A \cup B`

Answer: False

Reason: The strange looking "E" means "inside of" or "element of"

Set A U B is the union of sets A and B. The U basically means "or". We're looking to see if 7 is in set A, or set B, or both. Unfortunately, 7 is nowhere to be found in neither A nor B.