Mathematical Logic - Mathematical Logic

Which of the following propositions is tautology?

(p v q)→q

p v (q→p)

p v (p→q)

Both (b) & (c)

Answer Report Discuss

Option: C

Explanation :

A tautology is a statement that is always true.

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jigyasa gupta said: (11:54pm on Wednesday 20th March 2013)

evn in option b every condition is a tautology...

sanket said: (11:22am on Monday 15th April 2013)

why c is ans why not b

Nirmal said: (12:14am on Friday 7th June 2013)

Yes why not b?

Srushti said: (10:13pm on Thursday 11th July 2013)

without writing the truth table how to know whether it is tautology or no?

Nilesh said: (8:03am on Friday 5th June 2015)

[C] = P (P->q) = p ( ~p q )= p ~p q= ( p ~p ) q= True q= ( True q ) = True

Hina varshney said: (12:37pm on Tuesday 29th August 2017)

Option a is also tautology..

Jay said: (2:47am on Tuesday 19th September 2017)

D both(b and c)is tautology

stotaw takele said: (7:42am on Sunday 29th April 2018)

why not only b explain why include c

Arya said: (4:37am on Sunday 3rd June 2018)

B is answer

2: Which of the proposition is p^ (~ p v q) is

A.	A tautulogy
B.	A contradiction
C.	Logically equivalent to p ^ q
D.	All of above
	Answer Report Discuss
	Option: C Explanation : Click on Discuss to view users comments. ajinkya said: (10:03pm on Monday 1st July 2013) B'coz if u solve that eq. geting ans is same as that of p^q Amarnath said: (4:10pm on Wednesday 31st July 2013) ---------------------------------\| p \| q \|~p \|(~pvq)\|p^(~pvq)\|p^q\|---------------------------------\| 0 \| 0 \| 1 \| 1 \| 0 \| 0 \|---------------------------------\| 0 \| 1 \| 1 \| 1 \| 0 \| 0 \|---------------------------------\| 1 \| 0 \| 0 \| 0 \| 0 \| 0 \|---------------------------------\| 1 \| 1 \| 0 \| 1 \| 1 \| 1 \|---------------------------------So C is the right answer Akshita gupta said: (12:31am on Saturday 6th May 2017) Mah answer Contradiction(B) what is right answer B or C Sagar said: (4:06am on Thursday 15th February 2018) Ans is Tautologyin boolean algebra equivalent eq: p (p` q)= (p p`) q= 1 q= 1 (tautology). Write your comments here: Updating your Comments.. Updating your Comments..

3: Which of the following is/are tautology?

A.	a v b → b ^ c
B.	a ^ b → b v c
C.	a v b → (b → c)
D.	None of these
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	Option: B Explanation : Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

4: Logical expression ( A^ B) → ( C' ^ A) → ( A ≡ 1) is

A.	Contradiction
B.	Valid
C.	Well-formed formula
D.	None of these
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	Option: D Explanation : Click on Discuss to view users comments. Nilanshi Chauhan said: (7:09pm on Sunday 22nd October 2017) It is a tautology. Write your comments here: Updating your Comments.. Updating your Comments.. '>

5: Identify the valid conclusion from the premises Pv Q, Q → R, P → M, ˥M

A.	P ^ (R v R)
B.	P ^ (P ^ R)
C.	R ^ (P v Q)
D.	Q ^ (P v R)
	Answer Report Discuss
	Option: D Explanation : Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

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