English

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

Advertisements
Advertisements

Question

Prepare truth tables for the following statement pattern.

(~ p ∨ q) ∧ (~ p ∨ ~ q)

Sum

Solution

(~ p ∨ q) ∧ (~ p ∨ ~ q)

p q ~p ~q ~p∨q ~p∨~q (~p∨q)∧(~p∨~q)
T T F F T F F
T F F T F T F
F T T F T T T
F F T T T T T
shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Mathematical Logic - Exercise 1.6 [Page 16]

APPEARS IN

RELATED QUESTIONS

Express the following statement in symbolic form and write its truth value.

"If 4 is an odd number, then 6 is divisible by 3 "


Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`


Write converse and inverse of the following statement: 
“If a man is a bachelor then he is unhappy.” 


If p and q are true statements and r and s are false statements, find the truth value of the following :
( p ∧  ∼ r ) ∧ ( ∼ q ∧ s )


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


Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3."


Write the negation of the Following Statement :
∀ y ∈  N, y2 + 3 ≤ 7


State if the following sentence is a statement. In case of a statement, write down the truth value :
√-4 is a rational number.


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)


Prepare truth tables for the following statement pattern.

p → (~ p ∨ q)


Prepare truth table for (p ˄ q) ˅ ~ r

(p ∧ q) ∨ ~ r


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

~ p → (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)


Write the dual of the following:

p ∨ (q ∨ r) ≡ (p ∨ q) ∨ r


Write the dual statement of the following compound statement.

13 is prime number and India is a democratic country.


Write the dual statement of the following compound statement.

Radha and Sushmita cannot read Urdu.


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

(~p ∧ q) ∧ (~q ∨ ~r)


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

"If it snows, then they do not drive the car"


Construct the truth table for the following statement pattern.

(p ∨ ~q) → (r ∧ p)


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

[(p ∧ q) ∨ (~p)] ∨ [p ∧ (~ q)]


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

[(~p ∧ q) ∧ (q ∧ r)] ∨ (~q)


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

[~(p ∨ q) → p] ↔ [(~p) ∧ (~q)]


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

[~(p ∧ q) → p] ↔ [(~p) ∧ (~q)]


Using the truth table, prove the following logical equivalence.

[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r


Using the truth table, prove the following logical equivalence.

p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)


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

If a man is bachelor, then he is happy.


State the dual of the following statement by applying the principle of duality.

p ∨ (q ∨ r) ≡ ~[(p ∧ q) ∨ (r ∨ s)]


Write the dual of the following.

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)


Write the dual of the following.

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (q ∨ r)


Write the dual of the following.

~(p ∨ q) ≡ ~p ∧ ~q


Express the truth of the following statement by the Venn diagram.

Some members of the present Indian cricket are not committed.


Choose the correct alternative:

If p → q is an implication, then the implication ~q → ~p is called its


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


Which of the following is not equivalent to p → q.


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


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

(p ∧ q) → (q ∨ p)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×