Conditional Statements

A conditional sentence is a statement that states a proposition or theorem. Biconditional conditions are a more vital form of conditional statements, and Biconditional sentences are more substantial. If the front is actual, but the back is false, it’s true. Biconditional p iff, q is true if the statements have the same truth value of p is true. Otherwise, it’s false. It is indeed cold if it is snowing. Geometry uses conditional statements to create the same kind of conditional statements. If a polygon has four equal-length sides with four equal angles, it is a square. The conclusion and the hypothesis are the two parts of a conditional sentence.

Conditional Statement

It is also known as the material implied, implication, or material consequence.

The symbol for conditional connective is the right arrow.

Let’s say, for example, a doctor says that an apple can make you feel better. You could think of this statement as logical. There could be two propositions.

p: I will eat an apple

q: I will feel better

Based on the doctor’s advice, we could define a compound proposal that would read:

If p, then q

A compound proposition is written in symbolic logic:

p = q

Before we can look at the truth, there are many essential things you need to remember.

The connective (a right arrow) tells us the statement can only be read one way. There is one proposition on the left side of the arrow and another on the right. You cannot change these and expect that the meaning of the arrow will remain the same. You cannot say, for instance, that we feel better because we ate an apple.

The antecedent is p (ante meaning before), and the consequent is proposition q (think about what happens if you have p). The compound proposition states that the antecedent suggests the consequent or the consequent is presumed to have caused it.

The truth table for the conditional Statement

Two essential observations are necessary and urgent:

• Only one way
• If the antecedent and consequent are true, p=q will be false.
• If the subsequent is true, it does not matter what the actual value of the antecedent is.
• p=q is true.

It is essential to understand why the truth table looks like it does, row by row. While three of the four options make sense, row 3 seems counterintuitive.

Row 1 is simple. 

The doctor’s advice is correct if the apple makes you feel better. We can only assume that the apple eating and feeling better are causal; this could have been a coincidence or a placebo effect. We can say that it was a coincidence.

True is p=q

Row 2 also seems reasonable.

 Let’s say we eat an apple and don’t feel any better. The doctor was mistaken, and the condition was reinstated.

False is p=q

Row 4 is more complicated.

 If you don’t feel better after eating the apple, you can assume the doctor was right. According to the doctor, eating the apple will make you feel better. You didn’t follow the doctor’s advice, and you aren’t feeling better. You haven’t tested the doctor’s theory, so you can’t claim that the doctor’s advice wasn’t correct. You must assume the doctor’s words are actually in the absence of evidence.

Row 3 is the most troublesome. 

The doctor’s advice is valid if you do not eat the apple but feel better. Even though you feel better, you don’t have to prove that the doctor was wrong with his advice. According to the doctor, eating an apple would make you feel better. Guess what? You may have felt better. However, it doesn’t mean that you contradict what the doctor said.

Hypothesis in Geometry

A hypothesis is an assumption that a statement is true. Referring to the analogy of “if that, then that,” the hypothesis is the statement. The hypothesis is the basis of the statement. As you can see, the hypothesis is “a polygon with four equal-length sides” and “four equal angles.” The conclusion is the result of accepting the hypothesis, and part of the statement is the result of the hypothesis. In the geometry example, “it’s a square.”

Hypothesis Testing

Hypothesis testing in statistics is a method to test whether a claim is valid. The null hypothesis asserts no differences between the groups being studied. The alternative hypothesis asserts that there are differences between the groups being examined. The test statistic measures the probability that the null hypothesis will be valid. The value is the probability of the test statistic being as extreme as if there were a null hypothesis. If the value of p is lower than the alpha level, the null hypothesis should be rejected. The alternative hypothesis must be accepted.

Conclusion

There are many specific reasons why everyone should agree on the truth values of the conditional truth table, and hypothesis also gains to be a reason. We want a truth-functional kind of implication. We want only one possible interpretation if we construct a systematic symbolic logic. If we allow more than one interpretation, the implication ceases to be functional, and we lose all certainty in our conclusions. Now we will find the actual value of a statement like if P then Q solely based on the truth values of its components. The actual content of any proposition becomes irrelevant to the truth table, making it possible to construct absurd conditional statements and those that are far more plausible to accept.