4. If |P| = 25, Q = 30, R = 10, P Q = 10, Pn...

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4. If |P| = 25, Q = 30, R = 10, P Q = 10, Pn R = 5, Q R = 15, P Q R = 5. Find PUQUR. 5. A total of 1232 students have taken a course in Spanish, 879 have taken a course in French, and 114 have taken a course in Russian. Further, 103 have taken courses in both Spanish and French, 23 have taken courses in both Spanish and Russian, and 14 have taken courses in both French and Russian. If 2092 students have taken a course in at least one of Spanish French and Russian, how many students have taken a course in all 3 languages. 6. A survey of 100 students with respect to their choice of the ice cream flavours vanilla, chocolate and strawberry. Show that 50 students like vanilla, 43 like chocolate 28 like strawberry, 13 like vanilla and chocolate 11 like chocolate and strawberry, 12 like strawberry and vanilla and 5 like all of them. Find the number of students who like Vannila only Chocolate only Strawberry only Chocolate but not strawberry Chocolate and strawberry but not vanilla. Vannila or chocolate but not strawberry Also find the number of students who do not like any of these flavours (i) (ii) (iii) (iv) (v) (vi) 4. If |P| = 25, Q = 30, R = 10, P Q = 10, Pn R = 5, Q R = 15, P Q R = 5. Find PUQUR. 5. A total of 1232 students have taken a course in Spanish, 879 have taken a course in French, and 114 have taken a course in Russian. Further, 103 have taken courses in both Spanish and French, 23 have taken courses in both Spanish and Russian, and 14 have taken courses in both French and Russian. If 2092 students have taken a course in at least one of Spanish French and Russian, how many students have taken a course in all 3 languages. 6. A survey of 100 students with respect to their choice of the ice cream flavours vanilla, chocolate and strawberry. Show that 50 students like vanilla, 43 like chocolate 28 like strawberry, 13 like vanilla and chocolate 11 like chocolate and strawberry, 12 like strawberry and vanilla and 5 like all of them. Find the number of students who like Vannila only Chocolate only Strawberry only Chocolate but not strawberry Chocolate and strawberry but not vanilla. Vannila or chocolate but not strawberry Also find the number of students who do not like any of these flavours (i) (ii) (iii) (iv) (v) (vi)

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4solution Using the principle of inclusionexclusion we have PQR P Q R PQ PR QR PQR Given P 25 Q 30 R 10 PQ 10 PR 5 QR 15 PQR 5 Substituting these valu... View the full answer