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.
Write the truth values of the following.
64 is a perfect square and 46 is a prime number.
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.
Milk is white if and only if sky is blue.
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:
(q ∧ r) ∨ (∼ p ∧ s)
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∀ x ∈ A, x2 + x is an even number
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
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.
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.
`sqrt(-4)` 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.
He is an actor.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
1 is a prime number.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
The number 2 is the only even prime number.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Two co-planar lines are either parallel or intersecting.
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.
Which of the following statements is false?
Choose the correct alternative :
The statement (∼ p ∧ q) ∨∼ q 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 2 + 3 = 5 if and only if − 3 > − 9 is –––––––––.
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 :
Dual of (p ∧ ∼ q) ∨ t is (p ∨ ∼ q) ∨ C.
State whether the following statement is True or False :
Dual of “John and Ayub went to the forest” is “John and Ayub went to the forest”.
State whether the following statement is True or False :
Truth value of `sqrt(5)` is not an irrational number is T.
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.
Why are you sad?
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.
What a horrible sight it was!
Which of the following sentence is a statement? In case of a statement, write down the truth value.
0! = 1
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
∼ (p ∧ q) → ∼ (q ∧ p)
State the truth value of `sqrt(3)` is not an irrational number
State the truth value of (p ˅ ∼p)
If statements p, q are true and r, s are false, determine the truth values of the following.
~ p ∧ (q ∨ ~ r)
State whether the following statement is True or False:
p ↔ q is false when p and q have different truth values
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
The truth value of negation of “London is in England” is ______
Given following statements
p: 9 × 5 = 45
q: Pune is in Maharashtra
r: 3 is the smallest prime number
Write truth values by activity
|
i) (p ˄ q) ˄ r = `(square` ˄ `square)` ˄ `square` = `square` ˄ `square` = `square` ii) ~ ( p ˄ r ) = `~(square` ˄ `square)` = `~ square` = `square` iii) p → q = `square → square` = `square` |
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 ↔ (~ p → q) is false, 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.
Using truth table prove that:
`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`
