How many counterexamples does it take to show that a conditonal statement is false?

Mathematics

1 answer:

iren [92.7K]3 years ago

5 0

Answer:

one

Explanation:

First, note that a conditional statement in mathematics refers to a statement in which a hypothesis is given followed by a conclusion. Such as saying if P then "Q”, P and Q are sentences.

For example, a good example of conditional statement;

"If today is Sunday, then tomorrow is Monday"(hypothesis not underlined; condition underlined). While the counterexample could be one example or statement that satisfies the condition(s) of the statement but does not satisfy the conclusion.

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Two mechanics Worked on a car The first mechanic charge $55 per hour The second mechanic charge $80 per hour the mechanics work

Tems11 [23]

a = hours worked by the first mechanic

b = hours worked by the second mechanic.

since the first mechanic charges $55 per hour, then for "a" hours that'd be a total of 55*a or 55a, likewise, for the second mechanic that'd be a total charge of 80*b or 80b.

we know all hours combined are 15, so then a + b = 15.

we also know that all charges combined are $950, so 55a + 80b = 950.

$\bf \begin{cases} a+b=15\\ \boxed{b}=15-a\\ \cline{1-1} 55a+80b=950 \end{cases}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{55a+80\left( \boxed{15-a} \right)=950} \\\\\\ 55a+1200-80a=950\implies -25a+1200=950\implies -25a=-250 \\\\\\ a=\cfrac{-250}{-25}\implies \blacktriangleright a = 10\blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{b=15-a\implies }b=15-10\implies \blacktriangleright b=5 \blacktriangleleft$