Let A 2-3-5-7- Examine whether the statements given below are true or false-i - x - A such that x -3-9ii - x - A such that x is even-iii - x - A such that x -2-6-iv - x - A - x is prime- v - x - A - x -2-10vi - x - A - x -4 - 11

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Standard XII

Mathematics

Integration by Parts

Let A 2,3,5,7...

Question

Let $A {2, 3, 5, 7} .$ Examine whether the statements given below are true or false.

(i) $\exists x \in A$ such that $x + 3 > 9.$

(ii) $\exists x \in A$ such that x is even.

(iii) $\exists x \in A$ such that $x + 2 = 6.$

(iv) $\forall x \in A, x$ is prime.

(v) $\forall x \in A, x + 2 < 10$

(vi) $\forall x \in A, x + 4 \geq 11$

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Solution

(i) True (ii) True (iii) False (iv) True (v) True (vi) False

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Similar questions

Let $A = {1, 2, 3, 4} .$ Examine whether the statements given below are true or false.

(i) $\exists x \in A$ such that $x + 3 = 8.$

(ii) $\forall x \in A, x + 2 < 7.$

(iii) $\exists x \leftrightarrow A$ such that $x + 1 < 3.$

(iv) $\forall x \in A, x + 3 \geq 5.$

Q. If

A = {1, 2, 3, 4} .

, then number of statements from the below having truth value as true is

(1) \exists x \in A

such that

x + 3 = 8

(2) \forall x \in A, x + 2 < 7.

(3) \forall x \in A

such that

x + 1 < 3.

(4) \forall x \in A, x + 3 \geq 5.

Question 68

State whether the following statement is true or false:

If x and y are integers such that $x^{2} > y^{2}$ , then $x^{3} > y^{3}$

Question 68

State whether the following statement is true or false:

If x and y are integers such that $x^{2} > y^{2}$ , then $x^{3} > y^{3}$

f(x) and g(x) are continuous functions such that ${lim}_{x \to a} [3 f (x) + g (x)] = 6 a n d {lim}_{x \to a} [2 f (x) - g (x)] = 4$ . Given that the function h(x).g(x) is continuous at x = a and h(a)=4, which of the following must be true?

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Let A{2, 3, 5, 7}. Examine whether the statements given below are true or false. (i) ∃ x∈A such that x+3>9. (ii) ∃ x∈A such that x is even. (iii) ∃ x∈A such that x+2=6. (iv) ∀ x∈A, x is prime. (v) ∀ x∈A, x+2<10 (vi) ∀ x∈A, x+4≥11

(i) True (ii) True (iii) False (iv) True (v) True (vi) False