Classical

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

qp

pq

p v (pq)

p v (qp)

T

T

T

T

T

T

T

F

F

T

T

F

F

T

T

F

T

T

F

F

T

T

T

T

 

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ritu said: (9:06pm on Sunday 20th January 2013)
why c give some explaination
jigyasa gupta said: (9:54am on Thursday 21st March 2013)
evn in option b every condition is a tautology...
sanket said: (9:22pm on Monday 15th April 2013)
why c is ans why not b
badal said: (1:01am on Thursday 25th April 2013)
May i get full explanation about tautology
Nirmal said: (10:14am on Friday 7th June 2013)
Yes why not b?
Srushti said: (8:13am on Friday 12th July 2013)
without writing the truth table how to know whether it is tautology or no?
Nilesh said: (6:03pm 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: (10:37pm on Tuesday 29th August 2017)
Option a is also tautology..
Jay said: (12:47pm on Tuesday 19th September 2017)
D both(b and c)is tautology

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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
 
 

Option: C

Explanation :

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rekha malviya said: (7:55am on Sunday 5th May 2013)
why c..
ajinkya said: (8:03am on Tuesday 2nd July 2013)
B'coz if u solve that eq. geting ans is same as that of p^q
Amarnath said: (2:10am on Thursday 1st August 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: (10:31am on Saturday 6th May 2017)
Mah answer Contradiction(B) what is right answer B or C

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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
 
 

Option: B

Explanation :

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Srushti said: (8:17am on Friday 12th July 2013)
how its b?

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4:   Logical expression ( A^ B) → ( C' ^ A) → ( A ≡ 1) is
A. Contradiction
B. Valid
C. Well-formed formula
D. None of these
 
 

Option: D

Explanation :

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mukesh said: (12:14am on Friday 18th January 2013)
v
Nilanshi Chauhan said: (5:09am on Monday 23rd October 2017)
It is a tautology.

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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)
 
 

Option: D

Explanation :

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ritu said: (9:54pm on Sunday 20th January 2013)
how plzz explain
rekha malviya said: (8:02am on Sunday 5th May 2013)
how plz explain

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Syllabus covered in this section is-

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

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