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Given the following truth tables AND truth table OR truth table NOT table OR truth table NOT truth table input input output input input output

Given the following truth tables
AND truth table OR truth table NOT table OR truth table NOT truth table
input input output input input output input output
X Y XY X Y X+Y X X'
0 0 0 0 0 0 0 1
0 1 0 0 1 1 1 0
1 0 0 1 0 1
1 1 1 1 1 1
Using a truth table, prove that XZ=(X+Y)(X+Y)(X+Z)
X Y Z X+Y X+Y' X'+Z (X+Y)( XZ
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

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