**Inductive and deductive reasoning worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on inductive and deductive reasoning.

**Problem 1 :**

Sketch the next figure in the pattern.

**Problem 2 :**

Describe a pattern in the sequence of numbers. Predict the next number.

1, 4, 16, 64, ............

**Problem 3 :**

Let p be "the value of x is -5" and let q be "the absolute value of x is 5".

(i) Write p -> q in words.

(ii) Write q -> p in words.

(iii) Decide whether the biconditional statement p <-> q is true.

**Problem 4 :**

State whether the argument is valid.

Michael knows that if he misses the practice the day before a game, then he will not be a starting player in the game. Michael misses practice on Tuesday so he concludes that he will not be able to start in the game on Wednesday.

**Problem 5 :**

Write some conditional statements that can be made from the following true statements using the Law of Syllogism.

1. If a bird is the fastest bird on land, then it is the largest of all birds.

2. If a bird is the largest of all birds, then it is an ostrich.

3. If a bird is a bee hummingbird, then it is the smallest of all birds.

4. If a bird is the largest of all birds, then it is flightless.

5. If a bird is the smallest bird, then it has a nest the size of a walnut half-shell.

**Problem 1 :**

Sketch the next figure in the pattern.

**Solution : **

Each figure in the pattern looks like the previous figure with another row of squares added to the bottom. Each figure looks like a stairway.

So, the sixth figure in the pattern must have six squares in the bottom row.

**Problem 2 :**

Describe a pattern in the sequence of numbers. Predict the next number.

1, 4, 16, 64, ............

**Solution : **

Each number is four times the previous number.

So, the next number is 256.

**Problem 3 :**

Let p be "the value of x is -5" and let q be "the absolute value of x is 5".

(i) Write p -> q in words.

(ii) Write q -> p in words.

(iii) Decide whether the biconditional statement p <-> q is true.

**Solution : **

(i) If the value of x is -5, then the absolute value of x is 5.

(ii) If the absolute value of x is 5, then the value of x is -5.

(iii) The conditional statement in part (a) is true, but its converse in part (b) is false. So, the biconditional statement p <-> q is false.

**Problem 4 :**

State whether the argument is valid.

Michael knows that if he misses the practice the day before a game, then he will not be a starting player in the game. Michael misses practice on Tuesday so he concludes that he will not be able to start in the game on Wednesday.

**Solution : **

This logical argument is a valid use of the Law of Detachment. It is given that both a statement (p -> q) and its hypothesis (p) are true. So it is valid for Michael to conclude that the conclusion is true.

**Problem 5 :**

Write some conditional statements that can be made from the following true statements using the Law of Syllogism.

1. If a bird is the fastest bird on land, then it is the largest of all birds.

2. If a bird is the largest of all birds, then it is an ostrich.

3. If a bird is a bee hummingbird, then it is the smallest of all birds.

4. If a bird is the largest of all birds, then it is flightless.

5. If a bird is the smallest bird, then it has a nest the size of a walnut half-shell.

**Solution :**

Here are the conditional statements that use the Law of Syllogism.

a. If a bird is the fastest bird on land, then it is an ostrich. (Use 1 and 2.)

b. If a bird is a bee hummingbird, then it has a nest the size of a walnut half-shell. (Use 3 and 5.)

c. If a bird is the fastest bird on land, then it is flightless. (Use 1 and 4.)

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