A {x|€N and x is even number
Answers
Answer:
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Step-by-step explanation:
Even and Odd Numbers: A natural number (whole number) is an even number if it is a multiple of two. A natural number (whole number) that is not an even number is an odd number.
General Property:
A value of the form 2n, where n is a counting number (whole number), is an even number.
A value in the form of 2n – 1 where n is a counting number is an odd number.
A value in the form of 2n + 1 where n is a whole number is an odd number.
Note that an odd number is always one less (or one more) than some even number, 2n.
Set-Builder Notation:
The set of even counting numbers is {x : x = 2n where n ∈ N}.
The set of odd counting numbers is {x : x = 2n – 1 where n ∈ N}.
The set of even whole numbers is {x : x = 2n where n ∈ W}.
The set of odd whole numbers is {x : x = 2n + 1 where n ∈ W}.
Roster Notation:
The set of even counting numbers is {2, 4, 6, 8, 10, …}.
The set of odd counting numbers is {1, 3, 5, 7, 9, …}.
The set of even whole numbers is {0, 2, 4, 6, 8, 10, …}.
The set of odd whole numbers is {1, 3, 5, 7, 9, …}.
Answer:
Step-by-step explanation:
If A = { x : x € N and x < 20 } and
B = { x : x € N and x ≤ 5 } .
Write the set (A - B) in the set builder form.
Answer:
A - B = { x : x € N and 6 ≤ x ≤ 19 }
OR
A - B = { x : x € N and 5 < x < 20 }
Note:
• Set :-
A set is a well defined collection of distinct objects.
• Methods of representing a set :-
i. Roster or tabular or listed form
ii. Set-builder form
• Roster form :-
✓ All the elements are listed.
✓ Elements are separated by commas .
✓ Elements are enclosed within braces { } .
✓ The order of writing elements doesn't matter.
✓ The elements are not repeated.