Answer to Question #262693 in Discrete Mathematics for truc

Question

Prove the identity laws in Table 1 by showing that a) A U 0 A. b) A n U = A.

Answer 1

Solution:

(a) Assume $U=\{1,2,3,4,5,6\}, A=\{1,2,3\}$

To prove $A\cup \phi=A$

$LHS=A\cup \phi \\=\{1,2,3\} \cup \phi \\=\{1,2,3\} \\=A=RHS$

(b)

To prove $A\cap U=A$

$LHS=A\cap U \\=\{1,2,3\}A\cap \{1,2,3,4,5,6\} \\=\{1,2,3\} \\=A=RHS$

Hence, proved.