Decision Making Flashcards

A statement says: 'If it rains, the match is cancelled. The match was not cancelled.' What can be concluded?

Answer: It did not rain

This is modus tollens: if P → Q, and ¬Q, then ¬P. The match not being cancelled means it did not rain.

A pie chart shows: Category A = 30%, B = 45%, C = 25%. If total value = £2,000, what is the value of B minus A?

Answer: £300

B = 45% × £2,000 = £900. A = 30% × £2,000 = £600. B − A = £900 − £600 = £300.

In a class, 12 students study French, 15 study Spanish, and 5 study both. How many study at least one language?

Answer: 22

At least one = 12 + 15 − 5 = 22. Inclusion-exclusion removes the double count.

A logical puzzle: P is taller than Q. R is shorter than P. S is taller than R but shorter than Q. Who is second tallest?

Answer: P

Order from tallest: P > Q > S > R. P is tallest, Q is second tallest.

A factory produces 400 units per day. After a 15% efficiency improvement, how many units does it produce?

Answer: 460

400 × 1.15 = 460 units per day.

Which statement follows logically? 'No birds are reptiles. All parrots are birds. Snakes are reptiles.'

Answer: No parrot is a reptile

Since all parrots are birds and no birds are reptiles, no parrot can be a reptile. Follows by transitivity of set exclusion.