In a survey of 100 Enormous State University students, 25 enjoyed classical music, 20 enjoyed rock music, and 25 enjoyed house music. Five of the students enjoyed both classical and rock. How many of those that enjoyed rock did not enjoy classical music

The correct answer is 15.

Step-by-step explanation:

A survey is conducted of 100 Enormous State University students.

Number of students who enjoy only house music according to the question are 25 students.

Number of students who enjoy classical music according to the question are given to be 25.

Number of students who enjoy rock music according to the question are given to be 20.

Number of students who enjoy both rock and classical music according to the question are given to be 5.

Number of students who enjoyed only rock music are given by 20 - 5 = 15.

Thus 15 students enjoy rock and did not enjoy classical music.

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step-by-step explanation:

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< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)