Maths-
General
Easy
Question
Show the conjecture is false by finding a counterexample.
If the product of two numbers is positive, then the two numbers must both be positive.
The correct answer is: the given statement is false
We have given a statement If the product of two numbers is positive, then the two numbers must both be positive.
If we consider two positive numbers 7 and 9
Then , their product, 7 x 9 = 63
Hence, the statement is correct for positive integers
Suppose we take two negative integers - 7 and - 9
Then, their product, - 7 x - 9 = 63
So,The product of any two positive numbers is positive, and the product of any two negative numbers is also positive.
Therefore, the given statement is false.
Therefore, the given statement is false.
Related Questions to study
Maths-
Show the conjecture is false by finding a counterexample.
The square root of any positive integer x is always less than x.
Show the conjecture is false by finding a counterexample.
The square root of any positive integer x is always less than x.
Maths-General
Maths-
Show the conjecture is false by finding a counterexample.
All prime numbers are odd.
Show the conjecture is false by finding a counterexample.
All prime numbers are odd.
Maths-General
Maths-
Complete the conjecture.
The sum of the first n odd positive integers is ____.
Complete the conjecture.
The sum of the first n odd positive integers is ____.
Maths-General
Maths-
A square is drawn with the length of the side equal to the diagonal of the cube. if the square area is 72075 cm2, then find the side of the cube?
A square is drawn with the length of the side equal to the diagonal of the cube. if the square area is 72075 cm2, then find the side of the cube?
Maths-General
Maths-
What are all the possible values of b for which
is it factorable using only integer coefficients and constant?
What are all the possible values of b for which
is it factorable using only integer coefficients and constant?
Maths-General
Maths-
Find a counterexample to show that the following conjecture is false.
Conjecture: The square of any integer is always greater than the integer.
Find a counterexample to show that the following conjecture is false.
Conjecture: The square of any integer is always greater than the integer.
Maths-General
Maths-
Three blocks that are in the shape of a cube with each side 3.2 cm are attached end to end. Calculate the T.S.A of the resulting cuboid?
Three blocks that are in the shape of a cube with each side 3.2 cm are attached end to end. Calculate the T.S.A of the resulting cuboid?
Maths-General
Maths-
The area of a playground is
. Without removing common factors, factor to possible dimensions of the playground. How are the side-lengths related? What value would you need to subtract from the longer side and add to the shorter side for the playground to be a square?
The area of a playground is
. Without removing common factors, factor to possible dimensions of the playground. How are the side-lengths related? What value would you need to subtract from the longer side and add to the shorter side for the playground to be a square?
Maths-General
Maths-
What is the first three numbers in the pattern?
−, −, −, 64, 128, 256, …
What is the first three numbers in the pattern?
−, −, −, 64, 128, 256, …
Maths-General
Maths-
Calculate the maximum number of chocolates of size 2cmx3 cmx5 cm that can be kept in a rectangular box of dimensions 6cmx3cmx15 cm
Calculate the maximum number of chocolates of size 2cmx3 cmx5 cm that can be kept in a rectangular box of dimensions 6cmx3cmx15 cm
Maths-General
Maths-
Make and test a conjecture about the sign of the cube of negative integers
Make and test a conjecture about the sign of the cube of negative integers
Maths-General
Maths-
Given the area of a square, factor it to find the side length.
![text Area end text equals 144 x squared minus 24 x plus 1](data:image/png;base64,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)
Given the area of a square, factor it to find the side length.
![text Area end text equals 144 x squared minus 24 x plus 1](data:image/png;base64,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)
Maths-General
Maths-
Identify the value of c that makes the trinomial factorable using the perfect square pattern.
![x squared plus 16 x plus c](data:image/png;base64,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)
Identify the value of c that makes the trinomial factorable using the perfect square pattern.
![x squared plus 16 x plus c](data:image/png;base64,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)
Maths-General
Maths-
Given the area of a square, factor it to find the side length.
Area = ![36 x squared plus 120 x plus 100](data:image/png;base64,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)
Given the area of a square, factor it to find the side length.
Area = ![36 x squared plus 120 x plus 100](data:image/png;base64,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)
Maths-General
Maths-
Given five noncollinear points, make a conjecture about the number of ways to connect different pairs of points.
Given five noncollinear points, make a conjecture about the number of ways to connect different pairs of points.
Maths-General