Why is estimation an important tool ??

Mathematics

2 answers:

Valentin [98]3 years ago

6 0

It helps you plan ahead, and check your work to see if your answers make sense.

forsale [732]3 years ago

3 0

Estimation is a way to find out the approximation of something. It is important because it kinda leads to what the correct answer is and it is needed because you can estimate how much a bill would be or you could estimate how much is the area or size of something. It's very important...

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Can someone help me with this truth table. I just don't understand how to do it.

RUDIKE [14]

An implication $(p\implies q)$ is true if either the premise $(p)$ is false, or both the premise and conclusion $(p\text{ and }q)$ are both true, and false otherwise.

$\begin{array}{c|c|c|c|c|c|c}p&q&p\implies q&\neg q&(p\implies q)\land\neg q&\neg p&(p\implies q)\land\neg q\implies\neg p\\T&T&T&&&&\\T&F&F&&&&\\F&T&T&&&&\\F&F&T&&&&\end{array}$

Negation $(\neg q)$ is straightforward; if a statement is true, then its negation is false, and vice versa.

$\begin{array}{c|c|c|c|c|c|c}p&q&p\implies q&\neg q&(p\implies q)\land\neg q&\neg p&(p\implies q)\land\neg q\implies\neg p\\T&T&T&F&&F\\T&F&F&T&&F\\F&T&T&F&&T\\F&F&T&T&&T\end{array}$

A conjunction $(p\land q)$ is true if both premises are true, and false otherwise.

$\begin{array}{c|c|c|c|c|c|c}p&q&p\implies q&\neg q&(p\implies q)\land\neg q&\neg p&(p\implies q)\land\neg q\implies\neg p\\T&T&T&F&F&F\\T&F&F&T&F&F\\F&T&T&F&F&T\\F&F&T&T&T&T\end{array}$

Finally, by the rules of implication, we can fill the last column:

$\begin{array}{c|c|c|c|c|c|c}p&q&p\implies q&\neg q&(p\implies q)\land\neg q&\neg p&(p\implies q)\land\neg q\implies\neg p\\T&T&T&F&F&F&T\\T&F&F&T&F&F&T\\F&T&T&F&F&T&T\\F&F&T&T&T&T&T\end{array}$