Final answer:
The validity of an argument is based on logical structure, not just truth of premises. Without a specific conclusion provided in the question, we cannot determine the argument's validity. For full validity, the argument must have true premises and a conclusion that logically follows.
Step-by-step explanation:
The validity of an argument in logic is determined not by the truth of its premises but by the logical structure that connects the premises to the conclusion. A valid argument is one where if the premises are true, the conclusion must necessarily follow. Consequently, if an argument exhibits a form of logical reasoning such as a disjunctive syllogism, and if the premises given are true, then the conclusion that stems from these premises must be true as well.
Considering the statement in the question, 'If two angles are adjacent, then they share a side', and the general knowledge that adjacent angles do indeed share a common side, the argument seems to entail a valid form of reasoning. However, without a specific conclusion presented in the question, we cannot fully determine the argument's validity. For an argument to be valid, it requires not only correct premises but also a logical progression to a specific conclusion based on those premises.
In mathematics, such reasoning is crucial for coherence and consistency. For instance, when calculating the hypotenuse of a right triangle, regardless of whether we use the Pythagorean theorem or trigonometric functions, the conclusion (the calculated length of the hypotenuse) must agree, provided that we started with true premises (correct measurements of sides and angles).
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