In a single throw of a die describe the following events

Given: A dice is thrown once.

Let us find the given events, and also find A ∪ B, A ∩ B, B ∩ C, E ∩ F, D ∩ F and \( \overline{F}\)

S = {1, 2, 3, 4, 5, 6}

According to the subparts of the question, we have certain events as:

(i) A = getting a number below 7

So, the sample spaces for A are:

A = {1, 2, 3, 4, 5, 6}

(ii) B = Getting a number greater than 7

So, the sample spaces for B are:

B = {Փ}

(iii) C = Getting multiple of 3

So, the Sample space of C is

C = {3, 6}

(iv) D = Getting a number less than 4

So, the sample space for D is

D = {1, 2, 3}

(v) E = Getting an even number greater than 4.

So, the sample space for E is

E = {6}

(vi) F = Getting a number not less than 3.

So, the sample space for F is

F = {3, 4, 5, 6}

Now,

A = {1, 2, 3, 4, 5, 6} and B = {Փ}

A ⋃ B = {1, 2, 3, 4, 5, 6}

A = {1, 2, 3, 4, 5, 6} and B = {Փ}

A ⋂ B = {Փ}

B = {Փ} and C = {3, 6}

B ⋂ C = {Փ}

F = {3, 4, 5, 6} and E = {6}

E ⋂ F = {6}

E = {6} and D = {1, 2, 3}

D ⋂ F = {3}