Relations and Functions

Relations and Functions

Question

Let A = { a, b }, B = {a, b, c}. Is A ⊂ B? What is A ∪ B?

Answer

(a)   a  = {a, b}, B = {a,  b, c}
space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight a space element of space straight A comma space space space space space space space space space space rightwards double arrow space space space space space space straight a space element of space space straight B
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight b space element of space straight A comma space space space space space space space space space space space rightwards double arrow space space space space space straight b space element of space straight B

∴  Every number of set A is also a member of set B.

∴ space space space space space space space space space space space space space space space space space space space space space straight A space bottom enclose subset of space straight B
space space space space space space space space space space space space space space space space space space space space space Also comma space straight c element of straight B space and space straight c not an element of space straight A
space space space space space space space space space space space space space space space space space space space space space Hence comma space straight A space subset of space straight B
Also,    space space space space space space space space space space space space space space space space space straight A space union space straight B space equals space left curly bracket straight a comma space straight b right curly bracket space union space left parenthesis straight a comma space straight b comma space straight c right parenthesis space equals space left curly bracket straight a comma space straight b comma space straight c right curly bracket space equals space straight B
 

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