English

Construct the truth table for the following statement pattern. (~p ∨ q) ∧ (~p ∧ ~q) - Mathematics and Statistics

Advertisements
Advertisements

Question

Construct the truth table for the following statement pattern.

(~p ∨ q) ∧ (~p ∧ ~q)

Sum
Advertisements

Solution

p q ~p ~q ~p∨q ~p∧~q (~p∨q)∧(~p∧~q)
T T F F T F F
T F F T F F F
F T T F T F F
F F T T T T T
shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Mathematical Logic - Miscellaneous Exercise 1 [Page 33]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.11 | Page 33

RELATED QUESTIONS

Write the converse and contrapositive of the statement -
“If two triangles are congruent, then their areas are equal.”


Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]


Using the truth table prove the following logical equivalence.

∼ (p ∨ q) ∨ (∼ p ∧ q) ≡ ∼ p


Using the truth table proves the following logical equivalence.

∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p)


Examine whether the following statement pattern is a tautology or a contradiction or a contingency.

(p → q) ↔ (∼ p ∨ q)


Examine whether the following statement pattern is a tautology or a contradiction or a contingency.

[(p → q) ∧ ∼ q] → ∼ p


Determine whether the following statement pattern is a tautology, contradiction or contingency:

(p ∧ q) ∨ (∼p ∧ q) ∨ (p ∨ ∼q) ∨ (∼p ∧ ∼q)


Prepare truth tables for the following statement pattern.

(~ p ∨ q) ∧ (~ p ∨ ~ q)


Fill in the blanks :

Inverse of statement pattern p ↔ q is given by –––––––––.


Show that the following statement pattern is contingency.

(p∧~q) → (~p∧~q)


Prove that the following pair of statement pattern is equivalent.

p ↔ q and (p → q) ∧ (q → p)


Prove that the following pair of statement pattern is equivalent.

p → q and ~ q → ~ p and ~ p ∨ q


Write the dual statement of the following compound statement.

Karina is very good or everybody likes her.


Write the dual statement of the following compound statement.

A number is a real number and the square of the number is non-negative.


Write the negation of the following statement.

All the stars are shining if it is night.


Using the rules of negation, write the negation of the following:

~(p ∨ q) → r


Write the converse, inverse, and contrapositive of the following statement.

If he studies, then he will go to college.


Construct the truth table for the following statement pattern.

(p ∨ ~q) → (r ∧ p)


Using the truth table, prove the following logical equivalence.

p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)


Write the dual of the following.

~(p ∨ q) ≡ ~p ∧ ~q


The false statement in the following is ______.


Examine whether the statement pattern

[p → (~ q ˅ r)] ↔ ~[p → (q → r)] is a tautology, contradiction or contingency.


Complete the truth table.

p q r q → r r → p (q → r) ˅ (r → p)
T T T T `square` T
T T F F `square` `square`
T F T T `square` T
T F F T `square` `square`
F T T `square` F T
F T F `square` T `square`
F F T `square` F T
F F F `square` T `square`

The given statement pattern is a `square`


The statement pattern (p ∧ q) ∧ [~ r v (p ∧ q)] v (~ p ∧ q) is equivalent to ______. 


The equivalent form of the statement ~(p → ~ q) is ______.


Using truth table verify that:

(p ∧ q)∨ ∼ q ≡ p∨ ∼ q


The statement pattern (∼ p ∧ q) is logically equivalent to ______.


In the triangle PQR, `bar(PQ) = 2bara and bar(QR)` = `2 bar(b)` . The mid-point of PR is M. Find following vectors in terms of `bar(a) and bar(b)` .

  1. `bar(PR)`  
  2. `bar(PM)`
  3. `bar(QM)`

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×