Chapter 1: Sets

Exercise

Question

Question: 2 (vi)

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Examine whether the following statements are true or false:

(vi) {x : x is an even natural number less than 6} ⊂ {x : x is a natural number which divides 36}

Answer

1
Find the elements of the first set.
A = {x : x is an even natural{math_tip:def_natural_number} number less than 6} = {2, 4}
2
Find the elements of the second set.
B = {x : x is a natural{math_tip:def_natural_number} number which divides 36} = {1, 2, 3, 4, 6, 9, 12, 18, 36}
3
Determine whether all elements of the first set are also elements of the second set.
Answer: True
Reason: Every element of set A is present in set B. Therefore, the first set is a subset of the second set. Hence, the given statement is true.
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