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Complete the truth table. p q r q → r r → p (q → r) ˅(r → p) T T T T □ T T T F F □ □ T F T T □ T T F F T □ □ F T T □ F T F T T □ T □ F F F □ F T F F F □ T □ The given statement pattern is a □ - Mathematics and Statistics

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प्रश्न

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`

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उत्तर

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

The given statement pattern is a tautology.

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अध्याय 1.1: Mathematical Logic - Q.5

संबंधित प्रश्न

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

[(p→q) ∧ q]→p


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

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


Prove that the following statement pattern is equivalent :

(p ∨ q) →  r and (p → r) ∧ (q → r)


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


Show that the following statement pattern in contingency : 

(~p v q) → [p ∧ (q v ~ q)] 


Use the quantifiers to convert the following open sentence defined on N into true statement
5x - 3 < 10


Prove that the following statement pattern is equivalent:
(p v q) → r and (p → r) ∧ (q → r)


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p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]


Using the truth table prove the following logical equivalence.

[∼ (p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r


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 ∨ r)] ↔ ∼ [p → (q → r)]


Inverse of statement pattern (p ∨ q) → (p ∧ q) is ________ .


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

[p → (q → r)] ↔ [(p ∧ q) → r]


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

(p → q) ∨ (q → p)


Prepare truth tables for the following statement pattern.

(p ∧ r) → (p ∨ ~ q)


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

(~ q ∧ p) ∧ (p ∧ ~ p)


Prove that the following statement pattern is a tautology.

(p → q) ↔ (~ q → ~ p)


Prove that the following statement pattern is a contradiction.

(p → q) ∧ (p ∧ ~ q)


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(p∧~q) → (~p∧~q)


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~(p ∨ q) ∧ [p ∨ ~ (q ∧ ~ r)]


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(~p ∧ q) ∧ (~q ∨ ~r)


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(p → q) ∨ (p → r)


Using the truth table, prove the following logical equivalence.

[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r


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The false statement in the following is ______.


Choose the correct alternative:

If p is any statement, then (p ˅ ~p) is a


The converse of contrapositive of ∼p → q is ______.


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