Fill in the blanks : Conjunction of two statement p and q is symbolically written as ______. - Mathematics and Statistics

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Fill in the Blanks

Fill in the blanks :

Conjunction of two statement p and q is symbolically written as ______.

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Solution

Conjunction of two statement p and q is symbolically written as p ∧ q.

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Chapter 1: Mathematical Logic - Miscellaneous Exercise 1 [Page 30]

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r :
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(p ∧ q) ∨ r


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p → r


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q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
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∼ p ∨ q


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q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
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p→(q ∨ r)


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q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
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p → q


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

(p ∧ q) ∧ ∼ r


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r : Sachin is happy.
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∼ (p ∨ q) ∧ r


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~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


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If Kutab – Minar is in Delhi then Taj - Mahal is in Agra


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Even though it is not cloudy, it is still raining


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(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)


Write the negation of p → q


Choose the correct alternative:

Negation of p → (p ˅ ~q) is


Choose the correct alternative:

A biconditional statement is the conjunction of two ______ statements


State whether the following statement is True or False:

The converse of inverse of ~ p → q is q → ~ p


Negation of “Some men are animal “ is ______


Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”


Write the following statements in symbolic form.

If Qutub – Minar is in Delhi then Taj-Mahal is in Agra


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The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______


The statement, 'If I go to school, then I will get knowledge' is equivalent to ______ 


The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______ 


Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."


Let p, q and r be any three logical statements. Which of the following is true?


If p : A man is happy, q : A man is rich, then the symbolic form of ‘A man is neither happy nor rich is ______.


Converse of the statement q `rightarrow` p is ______.


Express the following compound statement symbolically:

Delhi is in India but Dhaka is not in Sri Lanka


Express the following compound statement symbolically:

3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25


Write the contrapositive of the inverse of the statement:

‘If two numbers are not equal, then their squares are not equal’.


From the following set of statements, select two statements which have similar meaning.

  1. If a man is judge, then he is honest.
  2. If a man is not a judge, then he is not honest.
  3. If a man is honest, then he is a judge.
  4. If a man is not honest, then he is not a judge.

If p, q are true statements and r, s are false statements, then write the truth value of the compound statement

(p `→` ∼ r) `→` (q ∧ s)


Using truth table prove that:

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


Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p


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