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**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**.

#### RELATED QUESTIONS

Discuss the statement pattern, using truth table : ~(~p ∧ ~q) v q

Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).

Write down the following statements in symbolic form :

(A) A triangle is equilateral if and only if it is equiangular.

(B) Price increases and demand falls

Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p

Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)

Write converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.

**Write the following compound statement symbolically.**

The angle is right angle if and only if it is of measure 90°.

Write the following compound statement symbolically.

Angle is neither acute nor obtuse.

Write the following compound statement symbolically.

Hima Das wins gold medal if and only if she runs fast.

Write the following compound statement symbolically.

x is not irrational number but is a square of an integer.

Construct the truth table of the following statement pattern.

[(p → q) ∧ q] → p

Construct the truth table of the following statement pattern.

(p ∧ ∼q) ↔ (p → q)

Construct the truth table of the following statement pattern.

(p ∧ q) ↔ (q ∨ r)

Construct the truth table of the following statement pattern.

p → [∼ (q ∧ r)]

Construct the truth table of the following statement pattern.

∼ p ∧ [(p ∨ ∼ q) ∧ q]

Construct the truth table of the following statement pattern.

(∼ p → ∼ q) ∧ (∼ q → ∼ p)

Construct the truth table of the following statement pattern.

(q → p) ∨ (∼ p ↔ q)

Construct the truth table of the following statement pattern.

(p ∨ ∼ q) → (r ∧ p)

Select and write the correct answer from the given alternative of the following question:

If p ∧ q is false and p ∨ q is true, then ______ is not true.

Construct the truth table of the following:

p → (q → p)

Construct the truth table of the following:

(∼p ∨ ∼q) ↔ [∼(p ∧ q)]

Construct the truth table of the following:

∼ (∼p ∧ ∼q) ∨ q

Construct the truth table of the following:

[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]

Construct the truth table of the following:

[(∼p ∨ q) ∧ (q → r)] → (p → r)

Determine the truth values of p and q in the following case:

(p ∨ q) is T and (p ∧ q) is T

Determine the truth values of p and q in the following case:

(p ∨ q) is T and (p ∨ q) → q is F

Determine the truth values of p and q in the following case:

(p ∧ q) is F and (p ∧ q) → q is T

**Express the following statement in symbolic form.**

Mango is a fruit but potato is a vegetable.

**Express the following statement in symbolic form.**

Milk is white or grass is green.

**Write the truth value of the following statement.**

The Himalayas are the highest mountains but they are part of India in the North East.

**Write the negation of the following statement.**

All men are animals.

**Write the negation of the following statement.**

2 + 3 ≠ 5

**Write the truth value of the negation of the following statement.**

London is in England.

**Write the following statement in symbolic form.**

If triangle is equilateral then it is equiangular.

**Write the following statement in symbolic form.**

Milk is white if and only if the sky is not blue.

**Find the truth value of the following statement.**

It is not true that 3 − 7i is a real number.

**Find the truth value of the following statement.**

If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.

**Find the truth value of the following statement.**

Every accountant is free to apply his own accounting rules if and only if machinery is an asset.

**Find the truth value of the following statement.**

Neither 27 is a prime number nor divisible by 4.

**Find the truth value of the following statement.**

3 is a prime number and an odd number.

**If p and q are true and r and s are false, find the truth value of the following compound statement.**

p ∧ (q ∧ r)

**If p and q are true and r and s are false, find the truth value of the following compound statement.**

[(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s]

Assuming that the following statement is true,

p : Sunday is holiday,

q : Ram does not study on holiday,

find the truth values of the following statements.

Sunday is not holiday or Ram studies on holiday.

Assuming that the following statement is true,

p : Sunday is holiday,

q : Ram does not study on holiday,

find the truth values of the following statements.

If Sunday is not holiday then Ram studies on holiday.

Assuming that the following statement is true,

p : Sunday is holiday,

q : Ram does not study on holiday,

find the truth values of the following statements.

Sunday is a holiday and Ram studies on holiday.

If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

**p ↔ ~ q**

**Fill in the blanks :**

Negation of “some men are animal” is –––––––––.

**State whether the following statement is True or False:**

The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.

**Assuming the first statement p and second as q. Write the following statement in symbolic form.**

The Sun has set and Moon has risen.

**Assuming the first statement p and second as q. Write the following statement in symbolic form.**

Mona likes Mathematics and Physics.

**Assuming the first statement p and second as q. Write the following statement in symbolic form.**

3 is prime number if 3 is perfect square number.

**Assuming the first statement p and second as q. Write the following statement in symbolic form.**

Kavita is brilliant and brave.

**Assuming the first statement p and second as q. Write the following statement in symbolic form.**

If Kiran drives the car, then Sameer will walk.

**Assuming the first statement p and second as q. Write the following statement in symbolic form.**

If a real number is not rational, then it must be irrational.

**Assuming the first statement p and second as q. Write the following statement in symbolic form.**

If the question paper is not easy then we shall not pass.

**If p : Proof is lengthy. ****q : It is interesting. ****Express the following statement in symbolic form.**

Proof is lengthy and it is not interesting.

**If p : Proof is lengthy. ****q : It is interesting. ****Express the following statement in symbolic form.**

If proof is lengthy then it is interesting.

**If p : Proof is lengthy. ****q : It is interesting. ****Express the following statement in symbolic form.**

It is not true that the proof is lengthy but it is interesting.

**If p : Proof is lengthy. ****q : It is interesting. ****Express the following statement in symbolic form.**

It is interesting iff the proof is lengthy.

**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.

Write the verbal statement of the following.

(p ∧ q) ∨ r

**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 → r

**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

**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)

**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

**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

**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

**Write the negation of the following.**

Kanchanganga is in India and Everest is in Nepal.

**Write the negation of the following.**

If x ∈ A ∩ B, then x ∈ A and x ∈ B.

**Rewrite the following statement without using the connective ‘If ... then’.**

If a quadrilateral is rhombus then it is not a square.

**Rewrite the following statement without using the connective ‘If ... then’.**

If 10 − 3 = 7 then 10 × 3 ≠ 30.

**Write the negation of the following statement.**

∀ n ∈ N, n + 3 > 9.

Negation of p → (p ˅ ∼ q) is ______

A biconditional statement is the conjunction of two ______ statements

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

Find the negation of 10 + 20 = 30

Write the following compound statements symbolically.

Triangle is equilateral or isosceles

Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p

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

Write the following statements in symbolic form

Even though it is not cloudy, it is still raining

Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)

Without using truth table show that -

(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

If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.

Given 'p' and 'q' as true and 'r' as false, the truth values of p v (q ∧ ~r) and (p → r) ∧ q are respectively

If q: There are clouds in the sky then p: it is raining. The symbolic form is ______

If p and q are true and rands are false statements, then which of the following is true?

Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______

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.

- If a man is judge, then he is honest.
- If a man is not a judge, then he is not honest.
- If a man is honest, then he is a judge.
- 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