Correct reasoning and problem solving
Answers are for parents and teachers.
1
“Every rose is a flower. This plant is a flower. So it is a rose.” Is the conclusion correct? Justify with a Venn diagram.
Wrong: the circle of roses lies inside the circle of flowers; the plant may be in the part of the flower circle outside the roses (for example a tulip).
2
Of 36 students, 24 play volleyball, 15 play table tennis and 5 play neither. How many play both?
8
3
n(A) = 30, n(B) = 28, n(C) = 26, n(A ∩ B) = 10, n(B ∩ C) = 9, n(A ∩ C) = 8, n(A ∩ B ∩ C) = 4. Find n(A ∪ B ∪ C).
61
4
In the sophism “7 · (10 − 5 · 2) = 9 · (10 − 5 · 2), cancelling gives 7 = 9”, where is the mistake?
10 − 5 · 2 = 0, so we cancelled zero; division by zero is impossible.
5
“If the phone’s battery runs out, the phone switches off. The phone did not switch off. So the battery has not run out.” Write the form and say whether it is correct.
((p ⇒ q) ∧ ¬q) ⇒ ¬p — modus tollens, correct.