Relations and Functions

Relations and Functions

Question

Given sets A = {1, 3, 5}, B = {2, 4, 6}, C = {0, 2, 4, 6, 8}, which of the following can be considered as universal set(s) of three sets A, B, C ?

(i) {0,1,2,3,4,5,6} (iii)ϕ

(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10} (iv) {1, 2, 3, 4, 5, 6, 7, 8}

Answer

Consider U= {0, 1, 2, 3, 4, 5, 6}
space space space space space space space space space space space space space space space space space space space space space space 8 space element of space straight C comma space but space 8 space not an element of space straight U subscript 1

∴  Uis not a universal set for A, B, C.
Consider : Uspace space space space space straight ϕ
None of members of sets A, B, C are members of set U2

∴ Uis not a universal set.
Consider  : U= {0, 1, 3, 4, 5, 6, 7, 8, 9, 10}
Every member of sets A, B  and C is a member of set U3. 
Hence U= {0, 1, 3, 4, 5, 6, 7, 8, 9, 10} is a universal set for sets A, B, C.
Consider                    U= {1, 2, 3, 4, 5, 6, 7, 8 }
space space space space space space space space space space space space space space space space space space space space space 0 space element of space straight C comma space but space 0 space not an element of space straight U subscript 4

∴  U is not a universal set sets A, B and C.
Hence,  the universal set is U= {0, 1, 3, 4, 5, 6, 7, 8, 9, 10}


 

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