7. in a music school of 124 students, 82 students play the piano, 71 students play the guitar and 10…
7. in a music school of 124 students, 82 students play the piano, 71 students play the guitar and 10 students play neither.\n7a construct a venn diagram to depict this situation.\na = \n\nb = \n\nc = \n\nd =
Answer
Explanation:
Step1: Find total students who play either
Total students: 124, neither: 10. So either = ( 124 - 10 = 114 ).
Step2: Let ( x ) be students who play both (B). Then piano only (C) = ( 82 - x ), guitar only (D) = ( 71 - x ). Total either: ( (82 - x) + x + (71 - x) = 114 ).
Simplify: ( 153 - x = 114 ) → ( x = 153 - 114 = 39 ) (B). Piano only (C): ( 82 - 39 = 43 ). Guitar only (D): ( 71 - 39 = 32 ). A is the universal set (all students), so A = 124.
Answer:
A = 124
B = 39
C = 43
D = 32
(For the Venn diagram: A is the rectangle (universal set, 124 students), C is piano only (43), B is both (39), D is guitar only (32), and the 10 who play neither are outside the circles but within A.)