Every positive even integer is of the form ____ for some integer ‘q’.
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2
IN AN EVEN INTEGER Q IS DIVISIBLE BY P
AND Q US SMALLER THAN P
AND Q US SMALLER THAN P
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We know that an integer is said to be even when it is divisible by 2.
Let q be a integer i.e. q = -1, 0, 1, 2, 3, 4,…..
Multiplying both the sides by 2
⇒ 2q = -2, 0, 2, 4, 6, 8,.……
Adding 1 on both the sides
⇒ 2q + 1 = -2 + 1, 0 + 1, 2 + 1, 4 + 1, 6 + 1, 8 + 1,…..
⇒ 2q + 1 = -1, 1, 3, 5, 7, 9,….
Hence, for some integer m, every even integer is of the form 2q
Let q be a integer i.e. q = -1, 0, 1, 2, 3, 4,…..
Multiplying both the sides by 2
⇒ 2q = -2, 0, 2, 4, 6, 8,.……
Adding 1 on both the sides
⇒ 2q + 1 = -2 + 1, 0 + 1, 2 + 1, 4 + 1, 6 + 1, 8 + 1,…..
⇒ 2q + 1 = -1, 1, 3, 5, 7, 9,….
Hence, for some integer m, every even integer is of the form 2q
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