Advertisements
Advertisements
Question
The dual of the statement (p ˅ q) ˄ (r ˅ s) is ______.
Options
(p ˄ q) ˄ (r ˄ s)
(p ˄ q) ˅ (r ˄ s)
(p ˅ q) ˅ (r ˅ s)
(p ˅ q) ˄ (r ˅ s)
Advertisements
Solution
The dual of the statement (p ˅ q) ˄ ( r ˅ s) is (p ˄ q) ˅ (r ˄ s).
Explanation:
The dual of a proposition that contains only the logical operators ∨, ∧ can be obtained by replacing each ∨ by ∧ and each ∧ by ∨.
RELATED QUESTIONS
Write the truth values of the following.
It is not true that 5−3i is a real number.
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)] ∨ [(q ∧ r) ∨ (p ∧ 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:
cos2θ − sin2θ = cos2θ for all θ∈R.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
With the sunset the day ends.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
The number π is an irrational number.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Bring the motor car here.
Which of the following is not a statement?
Choose the correct alternative:
Which of the following is always true?
Fill in the blanks :
Truth value of 2 + 3 = 5 if and only if − 3 > − 9 is –––––––––.
State whether the following statement is True or False :
“His birthday is on 29th February” is not a 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.
(2 + 1)2 = 9.
Solve the following :
State which of the following sentences are statements in logic.
Why are you sad?
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 quadratic equation ax2 + bx + c = 0 (a ≠ 0) always has two real roots.
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) → ∼ (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 ∧ ∼ q)]
If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.
∀ x ∈ A, x2 < 18.
Which of the following statement is true
If p is any statement then ( p ˅ ∼ p) is a
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r).
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` |
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.
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.
