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Logical Reasoning

How can you find a fake coin with a balance scale? How can you use math to pretend to read minds? Solve these puzzles and build your foundational logical reasoning skills.

Propositional Logic Word Problems

         

Consider the following three statements: \[\begin{align} \text{I}&. \text{ Those who like paintings like flowers.}\\ \text{II}&. \text{ Those who like running like music.}\\ \text{III}&. \text{ Those who do not like music do not like flowers.}\\ \end{align}\] If these are all true, which of the following statements must be true?

  1. Those who like running like flowers.
  2. Those who like paintings like music.
  3. Those who like flowers do not like running.
  4. Those who like running do not like paintings.
  5. Those who like paintings like running.

If Danny owns a bike, then Edward owns a bike. If Edward owns a bike, then Freddy owns a bike. If Danny owns a bike, which of the following statements must be true?

I. Edward owns a bike.
II. Freddy owns a bike.
III. Freddy does not own a bike.

A) I only
B) II only
C) III only
D) I and II only
E) I and III only

Whenever an aspiring author writes on her blog, she writes every day for 3 straight consecutive days and then rests on the following day.

During one particular week, she wrote on Thursday, Friday, and Saturday.

Did she write on her blog the Wednesday of this same week?

If Aria went to the school play, then Barney also went to the school play.
If Barney went to the school play, then Carie also went to the school play.
If Barney did not go to the school play, which of the following must be true?

I. Aria went to the school play.
II. Carie went to the school play.
III. Aria did not go to the school play.

A) I only
B) III only
C) I and II only
D) II and III only
E) None of the statements

We know that:

  • To make a cake, we must use baking powder.
  • Some cakes use strawberry as a topping.

I've made a cake.

What can we say about the following statement?

"I used both baking powder and strawberry for my cake."

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