# Mathematical Logic - Mathematical Logic

1:

Which of the following propositions is tautology?

A.

(p v q)→q

B.

p v (q→p)

C.

p v (p→q)

D.

Both (b) & (c)

Option: C

Explanation :

A tautology is a statement that is always true.

 q p q→p p→q p v (p→q) p v (q→p) T T T T T T T F F T T F F T T F T T F F T T T T

Click on Discuss to view users comments.

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)

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:
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 Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here:
4:   Logical expression ( A^ B) → ( C' ^ A) → ( A ≡ 1) is
 A. Contradiction B. Valid C. Well-formed formula D. None of these Answer Report Discuss 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: '>
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:

Syllabus covered in this section is-

• Propositional Logic
• First Order Logic
• Well-formed-formulae (WFFL)
• Satisfiability and Tautology

This Section covers Mathematical Logic Questions Answers

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