350 students were asked if they liked soccer or football. 200 said they liked soccer, and 180 said they liked football. how many students liked both soccer and football?

Number of students liked both soccer and football is 30.

Step-by-step explanation:

Let student likes soccer represent by A and student likes football represent by b.

Total student = A ∪ B

Student liking both sports = A ∩ B

Given:

Total number of students, n( A ∪ B ) = 350.

Number of student likes soccer,  n ( A )= 200

Number of student likes football,  n ( B ) = 180

To find Number of student likes both soccer and football, n( A ∩ B )

We use the following relation,

n ( A ∪ B ) = n ( A ) + n ( B ) - n ( A ∩ B )

350 = 200 + 180 - n ( A ∩ B )

n ( A ∩ B ) = 380 - 350

n ( A ∩ B ) = 30

Therefore, Number of students liked both soccer and football is 30.

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step-by-step explanation: