Question

Is every POSITIVE ODD integer of the form 2m-1? (where m is some integer) Explain.


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Answer 1

Answer:

No, the given statement is not true.

Step-by-step explanation:

For any positive odd integer, the general form is 2m-1 ∀ m ∈ N.

If m belongs to the set of integers (denoted by Z), then (2m - 1) will attain negative odd integers too.

For example: if m = -2 ⇒ (2m - 1) = -5 which is not a positive odd integer offcourse.

For any Positive Odd Integer, the general form is (2m-1) where m belongs to the set of Natural number whereas for any Negative Odd Integer, the general form is (2m-1) where m belongs to Non positive integers.

And in general Odd Integers are expressed as (2m-1) where m belongs to integers.

Additional Information:

Let's learn some common symbols and representations in set theory!

A set is a collection of well defined and distinct objects.

Set of Natural numbers is denoted by N

Set of Whole numbers is denoted by Z/I

Set of Real numbers is denoted by R

Set of Rational numbers is denoted by Q

Set of Irrational numbers is denoted by T

Set of complex numbers is denoted by C

Note: Complex numbers include both real and imaginary numbers.

Common symbols:

• ∈ Belongs to
• ⇒ Implies
• ∀ Forall
• ϕ (phi) used to represent empty set
• ∪ Union
• ∩ Intersection
• ⊂ Subset