Independent solution

How to solve this Events and Set Operations question

Setup

Setup

Represent the two yearly accident counts by nonnegative integers N1 and N2.

F={N1=1},G={N2≥1}F=\{N_1=1\},\qquad G=\{N_2\ge1\}
F∩G={N1=1, N2≥1}F\cap G=\{N_1=1,\ N_2\ge1\}

Model

Model

Compare each candidate with both defining restrictions, not merely with a subset of them.

(iii)={N1=1,N2≥1}=F∩G\text{(iii)}=\{N_1=1,N_2\ge1\}=F\cap G
(iv)={N1=1,N1+N2≥2}={N1=1,N2≥1}\text{(iv)}=\{N_1=1,N_1+N_2\ge2\}=\{N_1=1,N_2\ge1\}

Compute

Compute

The remaining statements either demand more than one second-year accident or fail to fix the first-year count.

(i)=(v)={N1=1,N2>1}⊊F∩G\text{(i)}=\text{(v)}=\{N_1=1,N_2>1\}\subsetneq F\cap G
(ii)={N1+N2≥2}⊋F∩G\text{(ii)}=\{N_1+N_2\ge2\}\supsetneq F\cap G

Answer

Answer

Two of the five listed events equal the intersection.

2events (C)\boxed{2\quad\text{events (C)}}