- #1
ayusuf
- 19
- 0
If A [tex]\subseteq[/tex] B does that mean A = B which means B = A because if A is a proper [tex]\subset[/tex] of B then A does not equal B right. I am wrong right?
ayusuf said:Yes exactly so if A [tex]\subseteq[/tex] B then every element in A must be in B
ayusuf said:and if A does not equal B then A is a proper [tex]\subset[/tex] of B.
ayusuf said:But everytime A [tex]\subseteq[/tex] B that must mean A = B right? If not please give me an example. Thanks.
ayusuf said:Right so from that example it would be wrong to say that A [tex]\subseteq[/tex] B but rather we should say A is a proper [tex]\subset[/tex] of B because A [tex]\neq[/tex] B.
[itex]A \subseteq B[/itex] means "A is a subset of B"; [itex]A \subset B[/itex] means "A is a subset of B and A is not equal to B." If [itex]A=B[/itex], it would be accurate to say [itex]A \subseteq B[/itex] but not [itex]A \subset B[/itex]. If [itex]A\ne B[/itex] and A is a subset of B, either would be fine.ayusuf said:Right so from that example it would be wrong to say that A [tex]\subseteq[/tex] B but rather we should say A is a proper [tex]\subset[/tex] of B because A [tex]\neq[/tex] B.
Sets are collections of objects or elements that share a common characteristic or property. They are used to organize and classify information in mathematics and other scientific fields.
Sets are typically represented using curly braces { } and listing the elements separated by commas. For example, the set of even numbers less than 10 can be represented as {2, 4, 6, 8}.
The symbol ≠ (not equal) is used to show that two sets are different, meaning they have different elements or properties. On the other hand, the symbol = (equal) shows that two sets are exactly the same, with the same elements and properties.
No, sets do not allow duplicate elements. Each element in a set must be unique.
Sets are closely related to other mathematical concepts such as functions, relations, and logic. They are also used in various branches of mathematics, including algebra, geometry, and probability.