Question

in a class of 50 students; 35 students play football 25 play both football as well as cricket . All students play atleast one game. how many students play only cricket? Show using Venn diagram.​

Answer 1

$\large\bf\underline {To \: find:-}$

• we need to find the number of students who play only cricket.

$\large\bf\underline{Given:-}$

• Total number of students = 50
• 35 students play's football
• 25 students play cricket as well as football.

$\huge\bf\underline{Solution:-}$

Let F denotes the set of people who plays football and C denotes the set of people who plays cricket.

So,

• n(F ∪ C) = 50
• n(F) = 35
• n(F ∩ C) = 25

we know that,

$\purple{ \underline{ \boxed{ \rm \: n(F \cap \: C) + n(F \cup \: C) = n(F) + n(C)}}}$

• n(F ∩ C) + n( F ∪ C) - n(F) = n(C)

➛ 25 + 50 - 35 = n(C)

➛ 75 - 35 = n(C)

➛ 40 = n(C)

so,

• 40 students plays cricket

Finding number of students who only plays cricket.

➛ n(C) = n(C ∩ F) + n(C - F)

➛ 40 = 25 + n(C - F)

➛ 40 - 25 = n(C - F)

➛ 15 = n(C - F)

➛ n(C - F) = 15

hence,

• ⚘ 15 students plays only cricket

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Answer 2

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Answer is in attachment.