Show that each conditional statement is a tautology using the fact that a conditional statement is false exactly when the hypothesis is true and the conclusion is false. (do not use truth tables.)

From Conditional Statements, there can be built a Tautology.

Step-by-step explanation:

According to the question, when the Hypothesis is True and the Conclusion is False, the result will be False. And that's correct.

But when Conditional Statement can be a Tautology, given the fact that not always a Conditional Statement will return the logic value of truth? Look at this example below:

1)James is from Orlando and He lives in Florida. Therefore, James is from Orlando.

2)James is from Orlando and He doesn't live in Florida. Therefore, James is from Orlando.

3)James is not from Orlando e He lives in Florida. Therefore, James is from Orlando

4)James is not from Orlando e He doesn't live in Florida. Therefore, James is from Orlando

What we have here above is symbolic for:

p∧q→p

And this is tautological, since no matter, we have on line 2 for p∧q, q being false it does not change the value for false, in any way for the whole proposition p∧q→p . What gives us a Tautology

This, p∧q→p can be rewritten as p∧q⇒p

yep

step-by-step explanation:

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.