Question

On the real axis, if A = [-1,1) and B = [0,4], then find the following:

I)A ∩ B II) A ∪ B​

Answer 1

Answer:

number of elements in A=10

Number of subsets of A containing exactly two elements

= Number of ways we can select 2 elements from 10 elements

10

C

2

=

2

10×9

=45

∴ Number of subsets of A containing exactly two elements =45

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Answer 2

Answer:

$A\cup B=\{-1, 0, 1, 2, 3, 4\}$ and $A\cap B=\{ 0, 1\}$  

Step-by-step explanation:

Concept:

• The real axis is the line in the complex plane, where the imaginary part is equal to zero.
• Therefore, every point on the line corresponds to a real number.
• If A and B are two sets, then the union of two sets is a set containing all elements that are in A and in B.
• If A and B are two sets, then the intersection of two sets is a set containing the elements that are common in A and B.              

Given:

The sets A and B on real axis, where A = [-1, 1] and B = [0, 4]

Solution:

On real axis, if A = [-1, 1] then A contains the integers from -1 to 1,

Therefore, the elements of A = {-1, 0, 1}.

if B = [0, 4] then B contains the integers from 0 to 4,

Therefore, the elements of B = {0, 1, 2, 3, 4}  

Then $A\cup B=\{-1, 0, 1\}\cup \{0, 1, 2, 3, 4\}$

$=\{-1, 0, 1, 2, 3, 4\}$

And $A\cap B=\{-1, 0, 1\}\cap \{0, 1, 2, 3, 4\}$

$=\{ 0, 1\}$

Conclusion:      

Therefore,  $A\cup B=\{-1, 0, 1, 2, 3, 4\}$ and $A\cap B=\{ 0, 1\}$ .