Question

Rewrite the following using mathematical symbols.

a. M is equal to the set whose elements are a, b, and r.
b. The set containing 9 and 11 is equal to the set containing 11 and 9.
c. The set containing 6 and 9 only is not a proper subset of
{5,6,12}

Answer 1

Mathematical notation for the provided statements would be M = {a, b, r}, {9, 11} = {11, 9}, and {6, 9} ⊄ {5, 6, 12}, representing set equality and the concept of proper subsets.

Step-by-step explanation:

To rewrite the statements using mathematical symbols, we would proceed as follows:

1. M is equal to the set whose elements are a, b, and r. This can be written as M = {a, b, r}.
2. The set containing 9 and 11 is equal to the set containing 11 and 9. This is expressed as {9, 11} = {11, 9}, demonstrating the commutative property of sets: the order of the elements does not affect the set identity.
3. The set containing 6 and 9 only is not a proper subset of {5,6,12}. This statement can be written as {6, 9} ⊄ {5, 6, 12}, whereby the symbol '⊄' indicates 'is not a proper subset of'.

Note that in set notation, the order of elements is not significant, and repeating elements are also ignored. The sets {9, 11} and {11, 9} are indeed identical.