The angle addition postulate is sometimes described as "the whole is equal to the sum of its parts." Explain how this descriptio
n applies to the angle addition postulate.
1 answer:
To explain this clearly, refer to the figure attached.
Angle addition, from the name itself, is the sum of the smaller angles to make up the bigger angle. In that case, the yellow angle plus the green angle, equals the maroon angle. As long as they have the same vertex (vertex O), you can add up angles that are side by side to obtain the value of the total angle. That is what the phrase <span>"the whole is equal to the sum of its parts" means.</span>
Angle addition, from the name itself, is the sum of the smaller angles to make up the bigger angle. In that case, the yellow angle plus the green angle, equals the maroon angle. As long as they have the same vertex (vertex O), you can add up angles that are side by side to obtain the value of the total angle. That is what the phrase <span>"the whole is equal to the sum of its parts" means.</span>
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Answer:
(i) A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.
Since A ∧ B (the symbol ∧ means A and B) is true only when both A and B are true, its negation A NAND B is true as long as one of A or B is false.
Since A ∨ B (the symbol ∨ means A or B) is true when one of A or B is true, its negation A NOR B is only true when both A and B are false.
Below are the truth tables for NAND and NOR connectives.
(ii) To show that (A NAND B)∨(A NOR B) is equivalent to (A NAND B) we build the truth table.
Since the last column (A NAND B)∨(A NOR B) is equal to (A NAND B) it follows that the statements are equivalent.
(iii) To show that (A NAND B)∧(A NOR B) is equivalent to (A NOR B) we build the truth table.
Since the last column (A NAND B)∧(A NOR B) is equal to (A NOR B) it follows that the statements are equivalent.
