# Set,elements.I can't figure out if the sets are equal {5;7}={1+6;1+4}

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### 3 Answers

We consider two sets are equal if all the elements in the sets are equal.

Let us compare the sets.

We have the set { 5, 7} Then, the elements are 5 and 7

Now the set { 1+6, 1+4 }. Then, the elements are 1+4 = 5 and 1+6 = 7

Then the all elements of both sets are the same.

**Then, both sets are equal.**

These sets are equal. They are equal because every element of the first set is also an element of the second set.

The elements in the second set are expressed differently, than the elements of the first set. But they are still the same elements -- 1 + 6 is 7, 1 + 4 is 5. And the order of the numbers in a set is not relevant. As long as the elements are the same, it doesn't matter what order they're in.

To state that the sets are equal, we'll have to determine the elements from the right side set.

{1+6;1+4}

We'll re-write this set, substituting the additions by their sums:

{1+6;1+4} = {7 ; 5}.

We know that 2 sets are equal if their elements are the same. We notice that the right side set has the same number of elements and the elements are the same, though the order of elemnts is reversed.

So, both sets are equal, no doubt about it!