The assignments are only the circled questions in the attached pdf

CamScanner 09-13-2021 13.19
203hw1-frq1zaib.pdf

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The assignments are only the circled questions in the attached pdfCamScanner 09-13-2021 13.19

Neha · Accepted Answer

Question 34
a) p -> not p
	p
	¬p
	p⇒¬p
	T
	F
	F
	F
	T
	T
b) p  ~q
	p
	q
	~q
	p≡ ¬q
	T
	T
	F
	F
	T
	F
	T
	T
	F
	T
	F
	T
	F
	F
	T
	F
c) P ⊕ (P v Q)
	p
	q
	P v q
	P⊕(P∨Q)
	T
	T
	T
	F
	T
	F
	T
	F
	F
	T
	T
	T
	F
	F
	F
	F
d) (p^q)->(pvq)
	p
	q
	p^q
	P v q
	p∧q⇒p∨q
	T
	T
	T
	T
	T
	T
	F
	F
	T
	T
	F
	T
	F
	T
	T
	F
	F
	F
	F
	T
e) q->~p (pq)
	p
	q
	~p
	Q => ~p
	q->~p (pq)
	T
	T
	F
	T
	F
	T
	F
	T
	F
	F
	F
	T
	F
	F
	F
	F
	F
	T
	T
	T
f) (pq) ⊕ (p~q)
	p
	q
	p≡q
	¬q
	p≡¬q
	(p≡q)⊕(p≡¬q)
	T
	T
	T
	F
	F
	T
	T
	F
	F
	T
	T
	T
	F
	T
	F
	F
	T
	T
	F
	F
	T
	T
	F
	T
Question 37
a) p-> not q
	p
	q
	Not q
	p⇒¬q
	T
	T
	F
	F
	T
	F
	T
	T
	F
	T
	F
	T
	F
	F
	T
	T
b) not p  q
	p
	q
	Not p
	¬p≡qx
	T
	T
	F
	F
	T
	F
	F
	T
	F
	T
	T
	T
	F
	F
	T
	F
c) (p->q) v(not p -> q)
	p
	q
	p⇒q
	¬p
	¬p⇒q
	(p⇒q)∨(¬p⇒q)
	T
	T
	T
	F
	T
	T
	T
	F
	F
	F
	T
	T
	F
	T
	T
	T
	T
	T
	F
	F
	T
	T
	F
	T
d) (p->q) ^(not p -> q)
	p
	q
	p⇒q
	¬p
	¬p⇒q
	(p⇒q)∨(¬p⇒q)
	T
	T
	T
	F
	T
	T
	T
	F
	F
	F
	T
	F
	F
	T
	T
	T
	T
	T
	F
	F
	T
	T
	F
	F
e) (pq)v(not p  q)
	p
	q
	p≡q
	¬p
	¬p≡q
	(p≡q)∨(¬p≡q)
	T
	T
	T
	F
	F
	T
	T
	F
	F
	F
	T
	T
	F
	T
	F
	T
	T
	T
	F
	F
	T
	T
	F
	T
f) (not p  not q)  (p q)
	p
	q
	¬p
	¬q
	¬p≡¬q
	p≡q
	¬p≡¬q≡p≡q
	T
	T
	F
	F
	T
	T
	T
	T
	F
	F
	T
	F
	F
	T
	F
	T
	T
	F
	F
	F
	T
	F
	F
	T
	T
	T
	T
	T
Question 41: (pq)(rs)
	p
	q
	r
	s
	p≡q
	r≡s
	p≡q≡r≡s
	T
	T
	T
	T
	T
	T
	T
	T
	T
	T
	F
	T
	F
	F
	T
	T
	F
	T
	T
	F
	F
	T
	T
	F
	F
	T
	T
	T
	T
	F
	T
	T
	F
	T
	F
	T
	F
	T
	F
	F
	F
	T
	T
	F
	F
	T
	F
	F
	T
	T
	F
	F
	F
	F
	T
	F
	F
	T
	T
	T
	F
	T
	F
	F
	T
	T
	F
	F
	F
	T
	F
	T
	F
	T
	F
	F
	T
	F
	T
	F
	F
	F
	T
	F
	F
	F
	T
	T
	T
	T
	T
	F
	F
	T
	F
	T
	F
	F
	F
	F
	F
	T
	T
	F
	F
	F
	F
	F
	F
	T
	T
	T
Question 18: ¬p∧(p⇒q)⇒¬q
	p
	q
	¬p
	p⇒q
	¬p∧(p⇒q)
	¬q
	¬p∧(p⇒q)⇒¬q
	T
	T
	F
	T
	F
	F
	T
	T
	F
	F
	F
	F
	T
	T
	F
	T
	T
	T
	T
	F
	F
	F
	F
	T
	T
	T
	T
	T
The value will change if values of p and q changes so it is not tautology
Question 26
(p->q)^(p->r) and p⇒(q∧r)
	p
	q
	r
	p⇒q
	p⇒r
	(p⇒q)∧(p⇒r)
	q∧r
	p⇒q∧r
	T
	T
	T
	T
	T
	T
	T
	T
	T
	T
	F
	T
	F
	F
	F
	F
	T
	F
	T
	F
	T
	F
	F
	F
	T
	F
	F
	F
	F
	F
	F
	F
	F
	T
	T
	T
	T
	T
	T
	T
	F
	T
	F
	T
	T
	T
	F
	T
	F
	F
	T
	T
	T
	T
	F
	T
	F
	F
	F
	T
	T
	T
	F
	T
Question 30: ¬p⇒(q⇒r)and q⇒p∨r
Question 35
We can say that the given statement is not logically equivalent.
Explanation:
Let there exist truth values for the three propositions p, q and r making the (p→q) → r false but the p → (q→ r) is true.
For this let take p is false, q is true and r is false. From this we get that (p → q) → r is false. That is here the premise (p → q) is true, and the conclusion r is false.
Where on the next side the ​​ p → (q → r) is true . Because the premise p is false.
Hence it is not logically equivalent.

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