State, giving reasons, which of the following pairs of sets are disjoi

1.	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’}
Answer» (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.

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’}

Answer»

(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.