State, giving reasons, which of the following pairs of sets are disjoint sets and which are or overlapping sets :

(i) A = {Girls with ages below 15 years} and B = {Girls with ages above 15 years}

(ii) C = {Boys with ages above 20 years} and D = {Boys with ages above 27 years}

(iii) A = {Natural numbers between 35 and 60} and B = {Natural numbers between 50 and 80}

(iv) P = {Students of class IX studying in I.C.S.E. Board} and Q = {Students of class IX}

(v) A = {Natural numbers multiples of 3 and less than 30} and B = {Natural numbers divisible by 4 and between 20 and 45}

(vi) P = {Letters in the word ‘ALLAHABAD’} and Q = {Letters in the word ‘MUSSOORIE’}

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1 Answers

(i) Disjoint sets; as no girl can be of age below 15 years and also above 15 years

(ii) Overlapping sets; as boys above 27 years are also above 20 years.

(iii) Overlapping sets; as natural numbers from 50 to 59 are common to both the sets.

(iv) Overlapping sets; as students of class IX studying in I.C.S.E. board are common.

(v) Overlapping sets; as natural number 24 is common to both the sets.

(vi) Disjoint sets; as no letter is common to both the sets.

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