Prove:
 
Ax(BUC)=(AxB)U(AxC)

Asked by Sthitaprajna Mishra | 22nd Jun, 2015, 11:14: PM

Expert Answer:

L e t space u s space c o n s i d e r space a n space e x a m p l e colon L e t space A equals open curly brackets 1 comma 2 comma 3 close curly brackets comma space B equals open curly brackets a comma b comma c comma d close curly brackets comma space C equals open curly brackets x comma y close curly brackets B union C equals open curly brackets a comma b comma c comma d comma x comma y close curly brackets A cross times open parentheses B union C close parentheses equals open curly brackets open parentheses 1 comma a close parentheses comma open parentheses 1 comma b close parentheses comma open parentheses 1 comma c close parentheses comma open parentheses 1 comma d close parentheses comma open parentheses 1 comma x close parentheses comma open parentheses 1 comma y close parentheses comma open parentheses 2 comma a close parentheses comma open parentheses 2 comma b close parentheses comma open parentheses 2 comma c close parentheses comma open parentheses 2 comma d close parentheses comma open parentheses 2 comma x close parentheses comma open parentheses 2 comma y close parentheses comma open parentheses 3 comma a close parentheses comma open parentheses 3 comma b close parentheses comma open parentheses 3 comma c close parentheses comma open parentheses 3 comma d close parentheses comma open parentheses 3 comma x close parentheses comma open parentheses 3 comma y close parentheses close curly brackets... left parenthesis 1 right parenthesis  A n d space A cross times B equals open curly brackets open parentheses 1 comma a close parentheses comma open parentheses 1 comma b close parentheses comma open parentheses 1 comma c close parentheses comma open parentheses 1 comma d close parentheses comma open parentheses 2 comma a close parentheses comma open parentheses 2 comma b close parentheses comma open parentheses 2 comma c close parentheses comma open parentheses 2 comma d close parentheses comma open parentheses 3 comma a close parentheses comma open parentheses 3 comma b close parentheses comma open parentheses 3 comma c close parentheses comma open parentheses 3 comma d close parentheses close curly brackets S i m i l a r l y space A cross times C equals open curly brackets open parentheses 1 comma x close parentheses comma open parentheses 1 comma y close parentheses comma open parentheses 2 comma x close parentheses comma open parentheses 2 comma y close parentheses comma open parentheses 3 comma x close parentheses comma open parentheses 3 comma y close parentheses close curly brackets T h u s comma space open parentheses A cross times B close parentheses union open parentheses A cross times C close parentheses equals open curly brackets open parentheses 1 comma a close parentheses comma open parentheses 1 comma b close parentheses comma open parentheses 1 comma c close parentheses comma open parentheses 1 comma d close parentheses comma open parentheses 2 comma a close parentheses comma open parentheses 2 comma b close parentheses comma open parentheses 2 comma c close parentheses comma open parentheses 2 comma d close parentheses comma open parentheses 3 comma a close parentheses comma open parentheses 3 comma b close parentheses comma open parentheses 3 comma c close parentheses comma open parentheses 3 comma d close parentheses comma open parentheses 1 comma x close parentheses comma open parentheses 1 comma y close parentheses comma open parentheses 2 comma x close parentheses comma open parentheses 2 comma y close parentheses comma open parentheses 3 comma x close parentheses comma open parentheses 3 comma y close parentheses close curly brackets... left parenthesis 2 right parenthesis F r o m space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space i t space i s space c l e a r space t h a t comma space A cross times open parentheses B union C close parentheses equals open parentheses A cross times B close parentheses union open parentheses A cross times C close parentheses

Answered by Vimala Ramamurthy | 23rd Jun, 2015, 11:14: AM