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kati45 [8]
2 years ago
15

Determine each of the following.

Mathematics
1 answer:
castortr0y [4]2 years ago
7 0

Answer:

(a) \{1,2,3,4,5,6,7,8,9,10\}

(b) 10

(c) \{\}

(d) 0

(e) 1024

Step-by-step explanation:

(a)

A = {x ∈ Z | 0 < x, x² ≤ 100}

We need to find all the elements of given set.

The given conditions are

0                ... (1)

x^2\leq 100

Taking square root on both sides.

-\sqrt{100}\leq x\leq \sqrt{100}

-10\leq x\leq 10             .... (2)

Using (1) and (2) we get

0

Since x ∈ Z,

A=\{1,2,3,4,5,6,7,8,9,10\}

(b)

We need to find the value of  | {x ∈ Z | 0 < x, x² ≤ 100}| or |A|. It means have to find the number of elements in set A.

|A|=10

| {x ∈ Z | 0 < x, x² ≤ 100}| = 10

(c)

B = {x ∈ Z | x > 10, x² ≤ 100}

We need to find all the elements of given set.

The given conditions are

x>10                ... (3)

x^2\leq 100

It means

-10\leq x\leq 10             .... (4)

Inequality (3) and (4) have no common solution, so B is null set or empty set.

B=\{\}

(d)

We need to find the value of |{x ∈ Z | x > 10, x² ≤ 100}| or |B|. It means have to find the number of elements in set B.

|B|=0

|{x ∈ Z | x > 10, x² ≤ 100}| = 0

(e)

We need to find the value of | P(A) |. P(A) is the power set of set A.

Number of elements of a power set is

N=2^n

where, n is the number of elements of set A.

We know that the number of elements of set is 10. So the value of |P(A)| is

|P(A)|=2^{10}

|P(A)|=1024

Therefore |P(A)|=1024.

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