Advertisements
Advertisements
प्रश्न
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.
उत्तर
Let p : x + y = 0 is the equation of a straight line.
q : y2 = 4x is the equation of the parabola.
The truth values of p and q are T and T respectively.
The given statement in symbolic form is p ↔ q.
∴ p ↔ q ≡ T ↔ T ≡ T
∴ Truth value of the given statement is T.
Notes
The answer in the textbook is incorrect.
APPEARS IN
संबंधित प्रश्न
State which of the following is the statement. Justify. In case of a statement, state its truth value.
The sunsets in the west
Write the truth values of the following.
It is not true that 5−3i is a real number.
If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:
∼ [(∼ p ∧ r) ∨ (s → ∼ q)] ↔ (p ∧ r)
If p ∧ q is F, p → q is F then the truth values of p and q are ________.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Did you eat lunch yet?
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
1 ! = 0
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!.
The negation of the proposition “If 2 is prime, then 3 is odd”, is ______
Choose the correct alternative :
If p is the sentence ‘This statement is false’ then
State whether the following statement is True or False :
Truth value of 2 + 3 < 6 is F.
State whether the following statement is True or False :
There are 24 months in year is a statement.
Solve the following :
State which of the following sentences are statements in logic.
(a + b)2 = a2 + 2ab + b2 for all a, b ∈ R.
Which of the following sentence is a statement? In case of a statement, write down the truth value.
a2 − b2 = (a + b) (a − b) for all a, b ∈ R.
Which of the following sentence is a statement? In case of a statement, write down the truth value.
What are the causes of rural unemployment?
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.
If stock prices are high then stocks are not rising.
Without using truth table show that
(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)
If p ↔ (~ p → q) is false, then the truth values of p and q are respectively ______.
If q Λ ∼p is T, then which of the following is correct?
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)`.
