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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 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

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.

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

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

Related Questions to study

Dimple Bought a Calculator and binder that were both 15% off the original price. Theoriginal price of binder was Rs 6.20. Justin spent a total of Rs 107. 27 . What was theoriginal price of the calculator?

Dimple Bought a Calculator and binder that were both 15% off the original price. Theoriginal price of binder was Rs 6.20. Justin spent a total of Rs 107. 27 . What was theoriginal price of the calculator?

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Complete the conjecture. The sum of the first n odd positive integers is ____.

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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.

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?

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?

Use the Law of Detachment to make a valid conclusion in the true situation.
If a number is odd, then its square is odd.
$x equals 7 text is odd end text$

Use the Law of Detachment to make a valid conclusion in the true situation.
If a number is odd, then its square is odd.
$x equals 7 text is odd end text$

Solve $fraction numerator 4 x over denominator 3 end fraction plus fraction numerator 2 x over denominator 3 end fraction equals x over 3 plus 5$

Solve $fraction numerator 4 x over denominator 3 end fraction plus fraction numerator 2 x over denominator 3 end fraction equals x over 3 plus 5$

Use the Law of Detachment to make a valid conclusion in the true situation.
Jim works every alternate day. He worked yesterday.

Use the Law of Detachment to make a valid conclusion in the true situation.
Jim works every alternate day. He worked yesterday.

Use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements.
If 𝑃 ⊆ 𝑄, then 𝑃 ⊆ 𝑅.
If 𝑃 ⊆ 𝑅, then 𝑃 ⊆ 𝑆.

Use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements.
If 𝑃 ⊆ 𝑄, then 𝑃 ⊆ 𝑅.
If 𝑃 ⊆ 𝑅, then 𝑃 ⊆ 𝑆.

Solve $fraction numerator 4 x over denominator 5 end fraction minus straight x equals x over 10 minus 9 over 2$

Solve $fraction numerator 4 x over denominator 5 end fraction minus straight x equals x over 10 minus 9 over 2$