मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

If p ↔ q and p → q both are true, then find truth values of the following with the help of activity p ˄ q p ↔ q and p → q both are true if p and q has truth value □, □ or □, - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

If p ↔ q and p → q both are true, then find truth values of the following with the help of activity

p ˄ q

p ↔ q and p → q both are true if p and q has truth value `square`, `square` or `square`, `square`

p ˄ q

i. If both p and q are true, then p ˄ q = `square` ˄ `square` = `square`

ii. If both p and q are false, then p ˄ q = `square` ˄ `square` = `square`

तक्ता
Advertisements

उत्तर

p ↔ q and p → q both are true if p and q has truth value T, T or F, F.

p ˄ q

i. If both p and q are true, then p ˄ q = T ˄ T = T

ii. If both p and q are false, then p ˄ q = F ˄ F = F

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.1: Mathematical Logic - Q.5

संबंधित प्रश्‍न

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


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

Congruent triangles are similar.


Write the truth values of the following.

4 is odd or 1 is prime.


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] ∨ [(q → p) → (∼ s ∨ r)]


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

∃ x ∈ A such that x2 < 0


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

π is an irrational number.


Write the truth value of the following statement:

∃ n ∈ N such that n + 5 > 10.


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.

Have a cup of cappuccino.


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

3 + 5 > 11


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

x2 - y2 = (x + y)(x - y) for all x, y ∈ R.


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

If a + b < 7, where a ≥ 0 and b ≥ 0 then a < 7 and b < 7.


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.


Fill in the blanks :

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


If p ∨ q is true then truth value of ∼ p ∨ ∼ q is ______.


Fill in the blanks :

Let p : the problem is easy. r : It is not challenging then verbal form of ∼ p → r is –––––––––.


State whether the following statement is True or False :

Dual of (p ∧ ∼ q) ∨ t is (p ∨ ∼ q) ∨ C.


Solve the following :

State which of the following sentences are statements in logic.
All integers are natural numbers.


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.

If 9 > 1 then x2 − 2x + 1 = 0 for x = 1


If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.

(p ∧ q) → ∼ p.


If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.

p ↔ (q → ∼ p)


Choose the correct alternative :

Which of the following statement is true?


Which of the following quantified statement is true?


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


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


Using truth table prove that:

`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×