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

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प्रश्न

Construct the truth table for the following statement pattern.

(p ∧ ~ q) ↔ (q → p)

बेरीज
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उत्तर

p q ~q p∧~q q→p (p∧~q)↔(q→p)
T T F F T F
T F T T T T
F T F F F T
F F T F T F
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पाठ 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३३]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.11 | पृष्ठ ३३

संबंधित प्रश्‍न

If   p : It is raining
     q : It is humid

Write the following statements in symbolic form:

(a) It is raining or humid.
(b) If it is raining then it is humid.
(c) It is raining but not humid. 


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


Show that the following statement pattern in contingency : 

(~p v q) → [p ∧ (q v ~ q)] 


By constructing the truth table, determine whether the following statement pattern ls a tautology , contradiction or . contingency.  (p →  q) ∧  (p ∧ ~ q ).


Using the truth table proves the following logical equivalence.

∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p)


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

(p → q) ∧ (p ∧ ∼q)


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

q ∨ [~ (p ∧ q)]


Prove that the following statement pattern is a tautology.

(p ∧ q) → q


Prove that the following statement pattern is a tautology.

(~ p ∨ ~ q) ↔ ~ (p ∧ q)


Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ ~p


Prove that the following statement pattern is a contradiction.

(p → q) ∧ (p ∧ ~ q)


Using the truth table, verify

p → (p → q) ≡ ~ q → (p → q)


Using the truth table, verify

~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Prove that the following pair of statement pattern is equivalent.

p → q and ~ q → ~ p and ~ p ∨ q


Write the dual of the following:

(p ∨ q) ∨ r


Write the dual of the following:

p ∨ (q ∨ r) ≡ (p ∨ q) ∨ r


Write the negation of the following statement.

Some continuous functions are differentiable.


With proper justification, state the negation of the following.

(p → q) ∨ (p → r)


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 ∨ r)] ↔ ~[p → (q → r)]


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

If 2 + 5 = 10, then 4 + 10 = 20.


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

(p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q)


Write the dual of the following.

(~p ∧ q) ∨ (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.


Write the converse and contrapositive of the following statements.

“If a function is differentiable then it is continuous”


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


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


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