Advertisements
Advertisements
Question
Write the truth value of the following statement:
∀ n ∈ N, n2 + n is even number while n2 – n is an odd number.
Advertisements
Solution
Let p: ∀ n ∈ N, n2 + n is an even number.
q: ∀ n ∈ N, n2 − n is an odd number.
Then the symbolic form of the given statement is p∧q.
The truth values of p and q are T and F respectively. ∴ The truth value of p∧q is F. ..........[T∧F ≡ F].
APPEARS IN
RELATED QUESTIONS
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.
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.
Can you speak in Marathi?
State which of the following is the statement. Justify. In case of a statement, state its truth value.
It rains heavily.
Write the truth value of the following.
If 3 × 5 = 8 then 3 + 5 = 15.
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)
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 x – 8 = 1
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∃ x ∈ A such that x2 < 0
If p ∧ q is F, p → q is F then the truth values of p and q are ________.
`sqrt5` is an irrational but `3sqrt5` is a complex number.
Write the truth value of the following statement:
The square of any even number is odd or the cube of any odd number is odd.
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.
A triangle has ‘n’ sides.
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.
Every real number is a complex number.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
x2 - y2 = (x + y)(x - y) for all x, y ∈ R.
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.
Can you speak in English?
Choose the correct alternative :
Which of the following is an open statement?
Choose the correct alternative :
If p : He is intelligent.
q : He is strong
Then, symbolic form of statement “It is wrong that, he is intelligent or strong” is
Choose the correct alternative :
The statement (∼ p ∧ q) ∨∼ q is
Choose the correct alternative :
∼ (p ∨ q) ∨ (∼ p ∧ q) is logically equivalent to
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 :
p ∧ t = p.
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.
x + 3 = 8 ; x is variable.
Determine the truth value of the following statement.
It is not true that 2 + 3 = 6 or 12 + 3 =5
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.
State the truth value of `sqrt(3)` is not an irrational number
State the truth value of (p ˄ ∼p)
State whether the following statement is True or False:
Mathematical identities are true statements
State whether the following statement is True or False:
p ˅ ~ p ≡ ~ c
The truth value of negation of “London is in England” is ______
The truth value of the statement “Neither 27 is a prime number nor divisible by 4” is ______
If the truth value of statement (q ∧ ~ r) → p is false (F), then the truth values of the statements p, q, rare respectively.
If truth values of p ↔ r, r, p ↔ q are F, T, F respectively, then respective truth values of p and q are ______.
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.
