Find the set A,B,C if AUB= {4,5,6,7} AUC={5,6,7,8} A intersection B= {5,6} A intersection C= {5,7}

Asked by Mayanglambamkalmax2526 | 21st Apr, 2020, 10:15: AM

Expert Answer:

To find A, B and C
G i v e n colon
A intersection B equals left curly bracket 5 comma space 6 right curly bracket space space a n d space space A intersection C equals left curly bracket 5 comma space 7 right curly bracket
rightwards double arrow 5 comma space 6 element of A intersection B space a n d space 5 comma space 7 element of A intersection C
rightwards double arrow 5 comma space 6 comma space 7 element of A space... space left parenthesis i right parenthesis
5 comma space 6 element of B
5 comma space 7 element of C
A l s o comma space g i v e n space A union B equals left curly bracket 4 comma space 5 comma space 6 comma space 7 right curly bracket space a n d space A union C equals left curly bracket 5 comma space 6 comma space 7 comma space 8 right curly bracket
I f space 4 element of A rightwards double arrow A union C space s h o u l d space c o n t a i n space 4 comma space b u t space 4 not an element of A union C rightwards double arrow 4 not an element of A space rightwards double arrow 4 element of B space... space left parenthesis F r o m space A union B right parenthesis
I f space 8 element of A rightwards double arrow A union B space s h o u l d space c o n t a i n space 8 comma space b u t space 8 not an element of A union B rightwards double arrow 8 not an element of A space rightwards double arrow 8 element of C space... space left parenthesis F r o m space A union C right parenthesis
rightwards double arrow A equals left curly bracket 5 comma space 6 comma space 7 right curly bracket comma space B equals left curly bracket 4 comma space 5 comma space 6 right curly bracket space a n d space C equals left curly bracket 5 comma space 7 comma space 8 right curly bracket

Answered by Renu Varma | 21st Apr, 2020, 10:58: AM