Advertisements
Advertisements
प्रश्न
If statements p, q are true and r, s are false, determine the truth values of the following.
(p ∧ ~r) ∧ (~q ∨ s)
Advertisements
उत्तर
(p ∧ ~r) ∧ (~q ∨ s)
≡ (T ∧ ∼F) ∧ (∼T ∨ F)
≡ (T ∧ T) ∧ (F ∨ F)
≡ T ∧ F
≡ F
∴ Truth value of (p ∧ ∼r) ∧ (∼q ∨ s) is F.
संबंधित प्रश्न
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.
Close the door.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Please get me breakfast.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
x2 = x
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Do you like Mathematics?
State which of the following is the statement. Justify. In case of a statement, state its truth value.
x2 – 6x – 7 = 0, when x = 7
State which of the following is the statement. Justify. In case of a statement, state its truth value.
It rains heavily.
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 A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∃ x ∈ A such that x2 < 0
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∀ x ∈ A, 2x + 9 > 14
If A = {1, 2, 3, 4, 5} then which of the following is not true?
Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:
Please get me a glass of water.
Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:
cos2θ − sin2θ = cos2θ for all θ∈R.
Write the truth value of the following statement:
∀ n ∈ N, n2 + n is even number while n2 – n is an odd number.
Write the truth value of the following statement:
In ΔABC if all sides are equal then its all angles are equal.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
x2 − 6x + 8 = 0 implies x = −4 or x = −2.
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.
Can you speak in English?
Choose the correct alternative:
Which of the following is always true?
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 :
p ↔ q is false when p and q have ––––––––– truth values.
State whether the following statement is True or False :
“His birthday is on 29th February” is not a statement.
Solve the following :
State which of the following sentences are statements in logic.
Ice cream Sundaes are my favourite.
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.
All integers are natural numbers.
Solve the following :
State which of the following sentences are statements in logic.
If x is real number then x2 ≥ 0.
Determine the truth value of the following statement.
4 + 5 = 7 or 9 − 2 = 5
Determine the truth value of the following statement.
If 9 > 1 then x2 − 2x + 1 = 0 for x = 1
Determine the truth value of the following statement.
x + y = 0 is the equation of a straight line if and only if y2 = 4x is the equation of the parabola.
Determine the truth value of the following statement.
It is not true that 2 + 3 = 6 or 12 + 3 =5
Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.
Stock prices are not high or stocks are rising.
Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.
Stock prices are high and stocks are rising if and only if stock prices are high.
Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.
It is false that stocks are rising and stock prices are high.
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
(p ∧ ∼ q) ∨ (∼ p ∧ q)
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
∼ [(p → q) ↔ (p ∧ ∼ q)]
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
Choose the correct alternative :
Which of the following statement is true?
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` |
If the truth value of statement (q ∧ ~ r) → p is false (F), then the truth values of the statements p, q, rare 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 ______.
The position vector of points A and B are `6bar(a) + 2bar(b) and bar(a) -3bar(b)` . If the point C divides AB in the ratio 3 : 2 then show that the position vector of C is 3`bar(a)- bar(b)`.
lf p, q are true statements and r, s are false statements, then find the truth value of ∼ (p ∧ ∼r) ∨ (∼q ∨ s).
