If a>b and a>c, then b>c
I do not get this question at all, I don't get counterexamples at all
So can you please help me :)
I do not get this question at all, I don't get counterexamples at all
So can you please help me :)
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A counter example is used to disprove something. If, for example, someone were to say, "If the grass is wet then it must have rained," then to disprove that statement all you need to do is find one example where the grass is wet but it didn't rain... like after the sprinklers go off. That's a counter example.
"If a > b and a > c, then b > c" is the statement you want to disprove, so all you need to do is find one counter example where that's not true.
Let a = 15, b = 5, and c = 10.
a > b? Sure... 15 > 5.
a > c? Sure... 15 > 10
b > c? Nope... 5 < 10.
The above is a counter example that disproves the statement. The first part is true (a > b and b > c), but the conclusion is false because b not > c.
"If a > b and a > c, then b > c" is the statement you want to disprove, so all you need to do is find one counter example where that's not true.
Let a = 15, b = 5, and c = 10.
a > b? Sure... 15 > 5.
a > c? Sure... 15 > 10
b > c? Nope... 5 < 10.
The above is a counter example that disproves the statement. The first part is true (a > b and b > c), but the conclusion is false because b not > c.
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If you have a statement in mathematics that you suspect is not true, the most straightforward way of showing that it is not true it to provide a counterexample.
For example, consider the statement "All numbers are even." Now that is definitely not a true statement. And in this case the fact that "the number 1 is odd" is a counterexample.
The problem you are posing claims that
if a > b and a > c, then b > c.
In words it claims that if one number is bigger than two other numbers, then the first of those two other numbers must be bigger than the second one. This is not true. For a counterexample consider
a = 3, b = 1 and c = 2.
Now a > b and a > c (since 3 > 1 and 3 > 2). However, b is not greater than c because 1 is not greater than 2. So this is a counterexample to the statement.
To recap a counterexample is just an example that proves a statement to be false.
For example, consider the statement "All numbers are even." Now that is definitely not a true statement. And in this case the fact that "the number 1 is odd" is a counterexample.
The problem you are posing claims that
if a > b and a > c, then b > c.
In words it claims that if one number is bigger than two other numbers, then the first of those two other numbers must be bigger than the second one. This is not true. For a counterexample consider
a = 3, b = 1 and c = 2.
Now a > b and a > c (since 3 > 1 and 3 > 2). However, b is not greater than c because 1 is not greater than 2. So this is a counterexample to the statement.
To recap a counterexample is just an example that proves a statement to be false.