A={x belongs to N: x is smaller than or equal to 3} and B={x belongs to W,x<2},find (A cross B) and (B cross A).Is (A cross B)=(B cross A)?

Asked by aashu.60 | 2nd Oct, 2015, 06:14: AM

Expert Answer:

G i v e n space t h a t space A equals open curly brackets x element of N colon x less or equal than 3 close curly brackets space a n d space B equals open curly brackets x element of W colon x less than 2 close curly brackets rightwards double arrow A equals open curly brackets 1 comma 2 comma 3 close curly brackets space a n d space B equals open curly brackets 0 comma 1 close curly brackets T h u s comma space A cross times B space i s space t h e space c a r t e s i a n space p r o d u c t space o f space A space a n d space B rightwards double arrow A cross times B equals open curly brackets open parentheses 1 comma 0 close parentheses comma open parentheses 1 comma 1 close parentheses comma open parentheses 2 comma 0 close parentheses comma open parentheses 2 comma 1 close parentheses comma open parentheses 3 comma 0 close parentheses comma open parentheses 3 comma 1 close parentheses close curly brackets A n d comma space B cross times A space i s space t h e space c a r t e s i a n space p r o d u c t space o f space B space a n d space A rightwards double arrow B cross times A equals open curly brackets open parentheses 0 comma 1 close parentheses comma open parentheses 1 comma 1 close parentheses comma open parentheses 0 comma 2 close parentheses comma open parentheses 1 comma 2 close parentheses comma open parentheses 0 comma 3 close parentheses comma open parentheses 1 comma 3 close parentheses close curly brackets I t space i s space v e r y space c l e a r space t h a t space A cross times B not equal to B cross times A

Answered by Vimala Ramamurthy | 2nd Oct, 2015, 12:03: PM