Given:

Number of students offered Mathematics = 50

Number of students offered Biology = 42

Number of students offered both Mathematics and Biology = 24

To Find:

(i) Number of students offered Mathematics only

Let us consider,

Number of students offered Mathematics = n(M) = 50

Number of students offered Biology = n(B) = 42

Number of students offered Mathematics & Biology both = n(M ∩ B) = 24

Number of students offered Mathematics only = n(M - B)

Venn diagram:

Now,

n(M - B) = n(M) – n(M ∩ B)

= 50 – 24

= 26

Therefore, Number of students offered Mathematics only= 26

(ii) Number of students offered Biology only

Number of students offered Biology only= n(B – M)

Now,

n(B – M) = n(B) – n(M ∩ B)

= 42 – 24

= 18

Therefore, Number of students offered Biology only = 18

(iii) Number of students offered any of two subjects

Number of students offered any of two subjects = n(M ∪ B)

Now,

n(M ∪ B) = n(M) + n(B) - n(M ∩ B)

= 50 + 42 – 24

= 140

Therefore, Number of students offered any of two subjects = 68