###### Advertisements

###### Advertisements

**Choose the correct alternative:**

A biconditional statement is the conjunction of two ______ statements

#### Options

Negative

Compound

Connective

Conditional

###### Advertisements

#### Solution

**Conditional**

#### APPEARS IN

#### RELATED QUESTIONS

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

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

**Using truth table, prove the following logical equivalence:**

(p ∧ q) → r ≡ p → (q → r)

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 truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p

Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)

Evaluate: ∫ x . log x dx

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.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu.

**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.

If Δ ABC is right-angled at B, then m∠A + m∠C = 90°

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) ↔ (p → q)

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 ∧ q) → r]

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

**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.**

It is false that Nagpur is capital of Maharashtra

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

`sqrt5` is an irrational number.

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

London is in England.

**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.**

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) ↔ ~(p ∨ q)

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

~ [p ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]

**Fill in the blanks :**

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

**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.**

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.**

The drug is effective though it has side effects.

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

It is not true that Ram is tall and handsome.

**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

**Rewrite the following statement without using conditional – **

(Hint : p → q ≡ ∼ p ∨ q)

If demand falls, then price does not increase.

**Write the negation of the following.**

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

**Write the negation of the following.**

Kanchanganga is in India and Everest is in Nepal.

**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.

**Consider the following statements.**

- If D is dog, then D is very good.
- If D is very good, then D is dog.
- If D is not very good, then D is not a dog.
- If D is not a dog, then D is not very good.

Identify the pairs of statements having the same meaning. Justify.

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

10 > 5 and 3 < 8

A biconditional statement is the conjunction of two ______ statements

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

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

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

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)

**Choose the correct alternative:**

Negation of p → (p ˅ ~q) is

**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 : Every natural number is a real number.

q : Every integer is a complex number. Then truth values of p → q and p ↔ q are ______ and ______ respectively.

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

If p, q are true statement and r is false statement, then which of the following statements is a true statement.

The symbolic form of the following circuit is (where p, q represents switches S_{1} and S_{2} closed respectively)

The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______

The inverse of the statement "If its quality is good. then it is expensive.", is ______

The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ______

The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______

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."

Conditional of p → q is equivalent to p → ∼ q.

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 ______.

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

It is not true that `sqrt(2)` is a rational number.

**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.

Using the statements

p: Seema is fat,

q: Seema is happy,

Write the following statements in symbolic form;

- Seema is thin and happy.
- If Seema is fat then she is unhappy.

Write the negation of (p `leftrightarrow` q).

**Using truth table prove that: **

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

Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p