###### Advertisements

###### Advertisements

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

p → q is equivalent to p → ~ q

#### Options

True

False

###### Advertisements

#### Solution

**False**

#### APPEARS IN

#### RELATED QUESTIONS

Write truth values of the following statements: ∃ n ∈ N such that n + 5 > 10.

Write the following statement in symbolic form and find its truth value:

∀ n ∈ N, n^{2} + n is an even number and n^{2} - n is an odd number.

Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency.

If p, q, r are the statements with truth values T, F, T, respectively then find the truth value of (r ∧ q) ↔ ∼ p

State which of the following is the statement. Justify. In case of a statement, state its truth value.

x – 3 = 14

State which of the following is the statement. Justify. In case of a statement, state its truth value.

Zero is a complex number.

State which of the following is the statement. Justify. In case of a statement, state its truth value.

Congruent triangles are similar.

A quadratic equation cannot have more than two roots.

Do you like Mathematics?

The sunsets in the west

All real numbers are whole numbers.

Can you speak in Marathi?

Write the truth values of the following.

4 is odd or 1 is prime.

Write the truth values of the following.

5 is a prime number and 7 divides 94.

Write the truth values of the following.

It is not true that 5−3i is a real number.

Write the truth value of the following.

If 3 × 5 = 8 then 3 + 5 = 15.

Write the truth value of the following.

Milk is white if and only if sky is blue.

Write the truth values of the following.

24 is a composite number or 17 is a prime number.

If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

p ∨ (q ∧ r)

If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

(p → q) ∨ (r → s)

If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

(p → q) ∧ ∼ r

[∼ p ∧ (∼ q ∧ r)] ∨ [(q ∧ r) ∨ (p ∧ r)]

∼ [(∼ p ∧ r) ∨ (s → ∼ q)] ↔ (p ∧ r)

If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∀ x ∈ A, x^{2} + x is an even number

If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∃ x ∈ A such that x^{2} < 0

If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∀ x ∈ A, x is an even number.

If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∀ x ∈ A, 2x + 9 > 14

If p ∧ q is F, p → q is F then the truth values of p and q are ________.

Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:

If x is a whole number then x + 6 = 0.

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

`sqrt5` is an irrational but `3sqrt5` is a complex number.

Write the truth value of the following statement:

In ΔABC if all sides are equal then its all angles are equal.

Write the truth value of the following statement:

∀ n ∈ N, n + 6 > 8.

**State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.**

Give me a compass box.

**State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.**

It may rain today.

**Choose the correct alternative :**

Which of the following is an open statement?

Which of the following statements is false?

**Choose the correct alternative :**

For the following three statements

p : 2 is an even number.

q : 2 is a prime number.

r : Sum of two prime numbers is always even.

Then, the symbolic statement (p ∧ q) → ∼ r means.

**Choose the correct alternative :**

If p : He is intelligent.

q : He is strong

Then, symbolic form of statement “It is wrong that, he is intelligent or strong” is

The negation of the proposition “If 2 is prime, then 3 is odd”, is ______

**Choose the correct alternative:**

Which of the following is always true?

**Choose the correct alternative :**

If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is

**Choose the correct alternative :**

Negation of the statement “This is false or That is true” is

**Fill in the blanks :**

The statement q → p is called as the ––––––––– of the statement p → q.

**Fill in the blanks :**

Truth value of if x = 2, then x2 = − 4 is –––––––––.

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

Truth value of 2 + 3 < 6 is F.

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

p ∨ q has truth value F is both p and q has truth value F.

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

x^{2} = 25 is true statement.

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

p ∧ t = p.

**Solve the following :**

State which of the following sentences are statements in logic.

x + 3 = 8 ; x is variable.

**Solve the following :**

State which of the following sentences are statements in logic.

Read a lot to improve your writing skill.

**Solve the following :**

State which of the following sentences are statements in logic.

z is a positive number.

**Solve the following :**

State which of the following sentences are statements in logic.

(a + b)^{2} = a^{2} + 2ab + b^{2} for all a, b ∈ R.

**Solve the following :**

State which of the following sentences are statements in logic.

(2 + 1)^{2} = 9.

**Solve the following :**

State which of the following sentences are statements in logic.

How beautiful the flower is!

**Solve the following :**

State which of the following sentences are statements in logic.

The square of any odd number is even.

**Solve the following :**

State which of the following sentences are statements in logic.

Do not come inside the room.

**Which of the following sentence is a statement? In case of a statement, write down the truth value.**

The square of every real number is positive.

**Which of the following sentence is a statement? In case of a statement, write down the truth value.**

a^{2} − b^{2} = (a + b) (a − b) for all a, b ∈ R.

**Which of the following sentence is a statement? In case of a statement, write down the truth value.**

Please carry out my instruction.

**Which of the following sentence is a statement? In case of a statement, write down the truth value.**

The Himalayas is the highest mountain range.

**Which of the following sentence is a statement? In case of a statement, write down the truth value.**

What are the causes of rural unemployment?

**Which of the following sentence is a statement? In case of a statement, write down the truth value.**

0! = 1

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

4 + 5 = 7 or 9 − 2 = 5

**If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.**

∃ x ∈ A, such that x + 3 < 11.

Which of the following statement is true

If p is any statement then ( p ˅ ∼ p) is a

State the truth value of `sqrt(3)` is not an irrational number

If statements p, q are true and r, s are false, determine the truth values of the following.

~ p ∧ (q ∨ ~ r)

If statements p, q are true and r, s are false, determine the truth values of the following.

(p ∧ ~r) ∧ (~q ∨ s)

The dual of the statement (p ˅ q) ˄ (r ˅ s) is ______.

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

Truth value of `sqrt(3)` is not an irrational number is F

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

(p ˅ q) ˄ ~ p is a contradiction

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

The dual of (p ˄ q) ˅ ~ q is (p ˅ q) ˄ ~ q

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

Mathematical identities are true statements

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

p ˅ ~ p ≡ ~ c

The truth value of negation of “London is in England” is ______

The truth value of the statement “Neither 27 is a prime number nor divisible by 4” is ______

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

**Without using truth table show that**

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

Given following statements **p:** 9 × 5 = 45 **q:** Pune is in Maharashtra **r:** 3 is the smallest prime number

Write truth values by activity

= `square` ˄ `square` = `square`
= `~ square` = `square`
= `square` |

Which of the following quantified statement is true?

Let a: ~ (p ∧ ~ r) v (~ q v s) and

b: (p v s) ↔ (q ∧ r).

If the truth values of p and q are true and that of rands are false, then the truth values of a and bare respectively.

The negation of 'For every real number x, `x^2 ≥ 0`' is ______

If (p ∧ ~ q) → ~ p is false, the truth values of p and q are respectively.

If the truth value of statement (q ∧ ~ r) → p is false (F), then the truth values of the statements p, q, rare respectively.

If p ↔ (~ p → q) is false, then the truth values of p and q are respectively ______.

If q Λ ∼p is T, then which of the following is correct?

If truth values of p ↔ r, r, p ↔ q are F, T, F respectively, then respective truth values of p and q are ______.

If p `rightarrow` (p ∧ ∼q) is false, then the truth values of p and q are respectively ______.

Consider the following two statements.

**Statement p:**

The value of sin 120° can be divided by taking θ = 240° in the equation 2 sin `θ/2` = `sqrt(1 + sin θ) - sqrt(1 - sinθ)`.

**Statement q:**

The angles A, B, C and D of any quadrilateral ABCD satisfy the equation `cos(1/2(A + C)) + cos(1/2(B + D))` = 0

Then the truth values of p and q are respectively.

If p : Every square is a rectangle. q : Every rhombus is a kite, then truth values of p `rightarrow` q and p `leftrightarrow` q are ______ and ______ respectively.

lf p, q are true statements and r, s are false statements, then find the truth value of ∼ (p ∧ ∼r) ∨ (∼q ∨ s).

**Using truth table prove that:**

`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`

**Find the truth value of the following compound statement:**

5 + 4 = 9 and 6 × 3 = 12