1. eXclusive-OR (XOR), denoted by the symbol, is a logical operation that performs the following Boolean...

 

Transcribed Image Text:

1. eXclusive-OR (XOR), denoted by the symbol, is a logical operation that performs the following Boolean operation: x+y = xy' + x'y XOR is 1 if x and y are the complements of each other. Using truth table or Boolean postulates, prove that XOR is: a. Commutative: x+y=yx a. Associative: x(y0z)=(xy) z=xyz 2. Prove that XOR is not distributive over AND, i.e., x(yz) (xy)(xz) 1. eXclusive-OR (XOR), denoted by the symbol, is a logical operation that performs the following Boolean operation: x+y = xy' + x'y XOR is 1 if x and y are the complements of each other. Using truth table or Boolean postulates, prove that XOR is: a. Commutative: x+y=yx a. Associative: x(y0z)=(xy) z=xyz 2. Prove that XOR is not distributive over AND, i.e., x(yz) (xy)(xz)