Which of the following pair of sets are not equal?

P = {1, 2, 3, 4} and Q = {x:x ϵ N and X < 5}

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P = {x:x² – 2x – 3 = 0}, and Q = {x:Xϵ N and X < 3}

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P = {15, 20, 25, 30, 35, 40} and Q = {x : x is a multiple of 5, 10 < x < 45}

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P = The set of prime numbers between 10 and 20 and Q = {11, 13, 17, 19}

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Solution

The correct option is B
P = {x:x² – 2x – 3 = 0}, and Q = {x:Xϵ N and X < 3}

Here P = {3,-1} and Q = {1,2}.Clearly P and Q does not have the same elements. Hence P and Q are not equal sets.

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Taking the set of natural numbers as the universal set, write down the complement of the following sets :

(i) {x : x is an even natural number}

(ii) {x : x is an odd natural number}

(iii) {x : x is a positive multiple of 3}

(iv) {x : x is a prime number}

(v) {x : x is a natural number divisible by 3 and 5}

(vi) {x : x is a perfect square}

(vii) {x : x is a perfect cube}

(viii) {x : x + 5 = 8}

(ix) {x : 2x + 5 = 9}

(x) {x : x $\geq$ 7}

(xi) {x : x $\in$ N and 2x + 1 > 10}

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