Deductive reasoning

If it rains, the match is cancelled. The match was not cancelled. What can you conclude?

• AIt did not rain✓
• BThe match was postponed
• CIt rained
• DIt might have rained

Answer: If rain always cancels the match and the match was not cancelled, then it did not rain (valid by contrapositive).

If the alarm sounds, everyone must leave the building. The alarm sounded. What follows?

• AThe alarm was faulty
• BEveryone must leave the building✓
• COnly staff must leave
• DSome people may stay

Answer: Given that the alarm sounded and the rule requires everyone to leave when it sounds, everyone must leave.

Tom is taller than Sara. Sara is taller than Ben. Who is the shortest?

• ACannot tell
• BSara
• CTom
• DBen✓

Answer: Tom is taller than Sara, who is taller than Ben, so Ben is the shortest.

All books on the top shelf are red. This book is blue. What can you conclude?

• AThis book is not on the top shelf✓
• BAll blue books are on the top shelf
• CThe top shelf has blue books
• DThis book is on the top shelf

Answer: Since every book on the top shelf is red and this book is blue, it cannot be on the top shelf.

Anna is older than Beth. Carl is younger than Beth. Who is the oldest?

• ACannot tell
• BBeth
• CCarl
• DAnna✓

Answer: Anna is older than Beth, and Carl is younger than Beth, so Anna is the oldest.

If a shape is a square, then it has equal sides. This shape does not have equal sides. What follows?

• AIt has three sides
• BIt is not a square✓
• CIt is a square
• DIt is a rectangle

Answer: By the contrapositive, if a square must have equal sides and this shape does not, then it is not a square.

Every day Maria takes the bus or walks. Today she did not walk. What follows?

• AShe stayed home
• BShe was late
• CShe cycled
• DShe took the bus✓

Answer: Since she either takes the bus or walks each day and she did not walk today, she took the bus.

In a queue, Raj is directly behind Sue, and Sue is directly behind Mia. Who is at the front?

• AMia✓
• BRaj
• CCannot tell
• DSue

Answer: Mia is ahead of Sue, who is ahead of Raj, so Mia is at the front of the queue.

Only ticket holders may enter. Jake entered the venue. What can you conclude?

• AJake works there
• BJake is a guest
• CJake is a ticket holder✓
• DJake bought food

Answer: Since only ticket holders may enter and Jake entered, Jake must be a ticket holder.

If the light is green, cars may go. The cars are not allowed to go. What follows about the light?

• AThe light is amber and green
• BThe light is green
• CThe light is not green✓
• DThe light is broken

Answer: If a green light always allows cars to go and they may not go, then the light is not green (contrapositive).

Three friends finish a race. Liam beats Noah. Owen finishes last. Noah is not last. What is the finishing order from first to last?

• ALiam, Noah, Owen✓
• BLiam, Owen, Noah
• COwen, Liam, Noah
• DNoah, Liam, Owen

Answer: Owen is last, and Liam beats Noah, so the order is Liam first, Noah second, Owen third.

Everyone who passed the test received a certificate. Priya did not receive a certificate. What follows?

• APriya retook the test
• BPriya lost her certificate
• CPriya passed the test
• DPriya did not pass the test✓

Answer: Since all who passed got a certificate and Priya did not get one, she did not pass.

A box contains only red and green balls. Every ball you draw is heavy. Red balls are light. What colour are the balls drawn?

• AA mix of red and green
• BRed
• CCannot tell
• DGreen✓

Answer: Since red balls are light but every drawn ball is heavy, the drawn balls cannot be red, so they must be green.

If you study hard, you will pass. You passed. Which statement is logically guaranteed?

• AYou studied hard
• BStudying hard alone is required to pass
• CYou did not study hard
• DNothing about whether you studied hard is guaranteed✓

Answer: Studying hard guarantees passing, but passing does not guarantee you studied hard, since other routes to passing may exist.

Four people sit in a row. Ann is left of Bob. Bob is left of Carl. Dan is right of Carl. Who is on the far right?

• ACarl
• BDan✓
• CBob
• DAnn

Answer: The order left to right is Ann, Bob, Carl, Dan, so Dan is on the far right.