Prove that (((p v ~q) ⊕ p) v ~p) ⊕ (p v ~q) ⊕ (p ⊕...
Prove that (((p v ~q) ⊕ p) v ~p) ⊕ (p v ~q) ⊕ (p ⊕ q) is
equivalent to p ^ q. Please show your work and name all the logical
equivalence laws for each step. ( v = or, ~ = not, ⊕ = XOR)
Thank you
Solutions
Expert Solution
Find the solution given in uploaded images (2 images are
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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!
Use Boolean algebraic laws to prove the following
equivalences:
[ ( p → q ) ∨ ( p → r ) ] ⟷ [ p ⟶ ( q ∨ r ) ]
¬ [ ¬ ( p ∧ q ) ∧ ( p ∨ q ) ] ↔ [ ( p → q ) ∧ ( q → p ) ]
If you are able to explain some of the thought process behind
the problems, that would be amazing. Thanks
(c) (¬p ∨ q) → (p ∧ q) and p
(d) (p → q) ∨ p and T
I was wondering if I could get help proving these expressions
are logically equivalent by applying laws of logic.
Also these 2 last questions im having trouble with.
Rewrite the negation of each of the following logical expressions
so that all negations
immediately precede predicates.
(a) ¬∀x(¬P(x) → Q(x))
(b) ¬∃x(P(x) → ¬Q(x))