Question

Asked Feb 15, 2019

Let A = {4, 6}, B = {6, 11, 23}, D = {35} and S = sample space = A ∪ B ∪ D. Identify Ac ∩ B.

a) {4, 11, 23}

b) {6, 35}

c) {6, 11, 23}

d) {11, 23}

e) {6}

f) None of the above.

Step 1

**Given information:**

The given events are as follows:

*A *= { 4, 6 }, *B *= { 6, 11, 23 }, *D *= { 35 } and the sample space is *S *= *A *∪ *B *∪ *D *= { 4, 6, 11, 23, 35 }.

*Complement of an event:*

Compliment of an event is all outcomes that are not in that event. The union of a particular event and compliment of that event gives all possible outcomes in the sample space for that event.

From the definition of compliment of an event it is known that the event *A ^{c }*consists of all the elements of the sample space and the elements that are not in

The formal notation of the elements of *A ^{c}* is given below:

Step 2

**Find the set of ***Ac**∩** B***:**

From the definition of compliment of an event, the event *Ac** ∩ B *consists of elements of *B *but not the elements of *A.*

In other words it can be said that, *Ac**∩ **B *is *B *– *A ∩ **B.*

The set o...

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