Question

# Show the conjecture is false by finding a counterexample. If the product of two numbers is even, then the two numbers must be even.

Hint:

### Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

## The correct answer is: Hence, the counterexample for the given conjecture is the product of 3 and 4

### Let the two numbers be x and y

Take x = 3 and y = 4

Multiplying x and y

x × y = 3 4

= 12

The result is an even integer but one of the number used in the product is 3 which is not even. So, the given conjecture i.e. “If the product of two numbers is even, then the two numbers must be even” is wrong.

Final Answer:

Hence, the counterexample for the given conjecture is the product of 3 and 4

### Related Questions to study

### Dimple Bought a Calculator and binder that were both 15% off the original price. The

original price of binder was Rs 6.20. Justin spent a total of Rs 107. 27 . What was the

original price of the calculator?

The x + 2 = 6 x+2=6x, plus, 2, equals 6 contains a variable. We call this type of equation with a variable an algebraic equation. Finding the variable value that will result in a true equation is typically our aim when solving an algebraic equation.

¶Variables or constants are the two types of measurable quantities. A variable is a quantity with a varying value, and the constant value is nothing but a constant.

¶**Steps to writing Variable Equation**

1) Identify the variables that represent the unknowns.

2) Convert the issue into variable expressions in algebra.

3) Determine the variables' values to solve the equations for their true values.

### Dimple Bought a Calculator and binder that were both 15% off the original price. The

original price of binder was Rs 6.20. Justin spent a total of Rs 107. 27 . What was the

original price of the calculator?

The x + 2 = 6 x+2=6x, plus, 2, equals 6 contains a variable. We call this type of equation with a variable an algebraic equation. Finding the variable value that will result in a true equation is typically our aim when solving an algebraic equation.

¶Variables or constants are the two types of measurable quantities. A variable is a quantity with a varying value, and the constant value is nothing but a constant.

¶**Steps to writing Variable Equation**

1) Identify the variables that represent the unknowns.

2) Convert the issue into variable expressions in algebra.

3) Determine the variables' values to solve the equations for their true values.