Which one of the following is not true.a)Successor of even number is a...
The predecessor of an even number is an odd number.
The successor of an even number is always an odd number. For example, after 26, 27 will come.
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Which one of the following is not true.a)Successor of even number is a...
Explanation:
To determine which statement is not true, we need to analyze each option and identify any contradictions or inconsistencies.
a) Successor of an even number is an odd number:
This statement is true. An even number can be defined as any number that is divisible by 2. When we add 2 to an even number, we get the next consecutive even number. Therefore, the successor of an even number will always be an odd number.
b) Predecessor of an odd number is an even number:
This statement is also true. An odd number can be defined as any number that is not divisible by 2. When we subtract 2 from an odd number, we get the previous consecutive odd number. Therefore, the predecessor of an odd number will always be an even number.
c) If a number is odd, its predecessor as well as successor will be even:
This statement is false. As mentioned above, the predecessor of an odd number is always an even number. However, the successor of an odd number will be the next consecutive odd number. Therefore, the successor of an odd number will also be odd.
d) An even number has an odd predecessor and an even successor:
This statement is also true. An even number can be defined as any number that is divisible by 2. When we subtract 2 from an even number, we get the previous consecutive even number. Therefore, the predecessor of an even number will always be an odd number. Similarly, when we add 2 to an even number, we get the next consecutive even number. Therefore, the successor of an even number will also be even.
e) None of these:
This option is not the correct answer because we have already determined that option D is the incorrect statement.
Therefore, the correct answer is option D because an even number does not have an odd predecessor and even successor.
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