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!
Explain the logical structure of the following set of
propositions - a theory.
1.The set of languages accepted (decided) by deterministic
Turing machines = the set of languages accepted (decided) by
nondeterministic Turing machines
2. PATH belongs to P
3. TAUTOLOGY is a member of coNP
4. 2 definitions for NP (1 in terms of a polynomial verifier 2
in terms of a nTM) are equivalent
5. PSPACE = NPSPACE
6. NP is a subset of PSPACE
7. SAT belongs...
Complete the following statements.Two compound propositions p and q in propositional logic are
logically equivalent if . . ..An argument form in propositional logic is valid if . . ..A theorem is a statement that . . ..A statement that is assumed to be true is called a(n) . . ..A proof is a valid argument that . . ..
Let p and q be the propositions
p:You drive over 65 miles per hour.
q: You get a speeding ticket.
Write these propositions using p and q and logical
connectives.
a) You do not drive over 65 miles per hour.
b) You drive over 65 miles per hour, but you do not geta
1
speeding ticket.
c) You will get a speeding ticket if you drive over
65 miles per hour.
d) If you do not drive over 65 miles...
The ‘Exclusive OR’ operation (also called XOR) between two
propositions p and q is defined as follows:
p ⊕ q = (p ∨ q) ∧ ¬(p ∧ q)
Using laws of propositional logic prove the following:
(i.) Exclusive OR is commutative, i.e., p ⊕ q ≡ q ⊕ p.
(ii.) p ⊕ p is a contradiction.
(iii.) Conjunction distributes over Exclusive OR, i.e, for any
proposition r,
r ∧ (p ⊕ q) ≡ (r ∧ p) ⊕ (r ∧ q)....
The ‘Exclusive OR’ operation (also called XOR) between two
propositions p and q is defined as follows:
p ⊕ q = (p ∨ q) ∧ ¬(p ∧ q)
Using laws of propositional logic prove that conjunction
distributes over Exclusive OR, i.e, for any proposition r,
r ∧ (p ⊕ q) ≡ (r ∧ p) ⊕ (r ∧ q).
Clearly state which law you are using in each step.