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Express in tabular method:

1. { x

\in

N : x² > 15 and x³ < 225 } ans: {4, 5, 6}

2. { x

\in

N : x is prime number and x < 8 }

Prove/Show that

Evaluate

\frac{f (\frac{1}{t^{2}}) + 1}{f (\frac{1}{t^{2}}) - 1}

when f(x) =

\frac{5 x^{2} + 3}{5 x^{2} - 3}

[dhaka board 2019]

* A = {

x \in N

: x is even and

x \leq 6

}

Evaluate P(A).

Show that if A has n elements, P(A) has 2ⁿ elements.

answer:

A = { 2, 4, 6 }

P(A) = { {}, {2}, {4}, {6}, {2, 4}, {2, 6}, {4, 6}, {2, 4, 6} }

Number of elements in A, n = 3

Number of elements in P(A) = 8 = 2³ = 2ⁿ .

problem: Given that B = {5, 7, 11, 13} - Determine P(B) to show that number of elements of P(B) is 2ⁿ , where n is the number of elements of B. (D.B. 2024)

P(B)=

{ϕ, {5}, {7}, {11}, {13}, {5, 7}, {5, 11}, {5, 13}, {7, 11}, {7, 13}, {11, 13}, {5, 7, 11}, {5, 7, 13}, {5, 11, 13}, {7, 11, 13}, {5, 7, 11, 13}}

problem: Determine the intersection set of all factors of 35 and 45. (R.B. 2024)

problem: If

C = {x \in N : x^{2} > 7 a n d x^{3} < 136}

Express

C

in roster method. (Ch.B. 2020)

C = {3, 4, 5}

problem: If

f (x) = \frac{1 + x^{3} + x^{6}}{x^{3}}

show that

f (x) = f (x^{- 2})

(C.B. 2024)

problem: Determine the solution set of

y^{2} = \sqrt{5} y

(B.B. 2024)

solution set = {value1, value2}

Sets and Functions