Set Theory: Equal Sets

Two sets, P and Q, are equal sets if they have exactly the same members. The order of elements in a set is not important.

Example :

List the elements of the following sets and show that P ≠ Q and Q = R.

P = {x : x is a positive integer and 5x ≤ 15}

Q = {x : x is a positive integer and x 2 < 25}

R = {x : x is a positive integer and x ≤ 4}

Solution :

5x ≤ 15 ⇒ x ≤ 3 So, P = {1, 2, 3}

x ² < 25 ⇒ x < 5 So, Q = {1, 2, 3, 4}

R = {1, 2, 3, 4}

Therefore, P ≠ Q and Q = R.

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