Advertisements
Advertisements
Question
State whether the following statement is True or False :
p ∨ q has truth value F is both p and q has truth value F.
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
| p | q | p ∨ q |
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
∴ The statement p ∨ q has the truth value F whenever both p and q have the truth value F.
APPEARS IN
RELATED QUESTIONS
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.
Congruent triangles are similar.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
x2 = x
Write the truth values of the following.
It is not true that 5−3i is a real number.
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 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.
The sum of interior angles of a triangle is 180°
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.
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.
The number of arrangements of 7 girls in a row for a photograph is 7!.
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.
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?
If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) 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 –––––––––.
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.
Why are you sad?
Solve the following :
State which of the following sentences are statements in logic.
If x is real number then x2 ≥ 0.
Which of the following sentence is a statement? In case of a statement, write down the truth value.
Every parallelogram is a rhombus.
Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.
If stock prices are high then stocks are not rising.
If p is any statement then ( p ˅ ∼ p) is a
State the truth value of `sqrt(3)` is not an irrational number
State the truth Value of x2 = 25
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` |
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.
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)`.
