In: Computer Science
Using logical equivalence laws, show that (((p v ~ q) ⊕ p) v ~p) ⊕ (p v ~q) is equivalent to p v q. v = or, ~ = not, ⊕ = exclusive or (XOR). Please show the steps with the name of the law beside each step, thanks so much!
[this is because from the definition of XOR we have
]
[this is because
]
[this is because
]
[this is because ]
[this is because
]
[this is because from the definition of XOR we have
]
[this is because
]
[this is because ]
[this is using the DeMorgan's Law
]
[this is obtained just by changing the parentheses]
[this is because
]
[this is because ]
[this is because ]
[this is from DeMorgan's Law
]
Proved