Deductive reasoning

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

• AIt rained
• BIt did not rain✓
• CThe match was postponed
• 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?

• ASome people may stay
• BEveryone must leave the building✓
• CThe alarm was faulty
• DOnly staff must leave

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?

• ATom
• BSara
• CBen✓
• DCannot tell

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 on the top shelf
• BThis book is not on the top shelf✓
• CAll blue books are on the top shelf
• DThe top shelf has blue books

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?

• AAnna✓
• BBeth
• CCarl
• DCannot tell

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

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 took the bus✓
• CShe cycled
• DShe was late

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?

• ARaj
• BSue
• CMia✓
• DCannot tell

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

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

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✓
• BNoah, Liam, Owen
• COwen, Liam, Noah
• DLiam, Owen, Noah

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

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