The exclusive or logical operation denoted p XOR q is it tru

The exclusive \"or\" logical operation, denoted p XOR q is it true when exactly one and ONLY one of either p, q is true; it is false when p and q are false and it is false when both p and q are true. a) create a truth table for p XOR q b) there is a relationship between XOR and \"symmetric difference\" as given in number 1. In a few sentences, describe this relationship in your own words.

Solution

a) The truth table is :

b) The symmetric difference of two sets is the set of elements which are in either of the sets and not in their intersection.

For a given object x, the symmetric difference of the sets P and Q is related to XOR as:

x (belongs to) (P (symmetric difference) Q) <=> (x (belongs to) P) XOR (x (belongs to) Q)

This relationship is quite obvious because XOR is true only when either one of the two is true and false whenever both are true or false which is equivalent to saying that it will belong to symmetric diff if it belongs to either one of the set but not if it either belongs to both or none of them.