11. Use De Morgan's laws to simplify the given expression.
¬(S∪T)'
Apply De Morgan's laws to (S∪T): Choose the correct answer below:
(S∪T)' = S'∩T' (S∪T)' = S∩T (S∪T)' = ST' (S∪T)' = S'∩T'
Simplify the given expression. ¬(S∪T)' = (Simplify your answer:)
12. Of the 124 students who took a mathematics exam, 57 correctly answered the first question, 60 correctly answered the second question, and 29 correctly answered both questions. How many students did not answer either of the two questions correctly?
students did not answer either of the two questions correctly:
13. Each of the 108 students attending a conservatory of music plays at least one of the piano, harp, and clarinet. 68 play the piano, 43 play the harp, 31 play the clarinet, 18 play the piano and the harp, 12 play the harp and the clarinet, and 9 play the piano and the clarinet. How many play all three instruments? Hint: Let x represent the number of students who play all three instruments.