Understanding Sets: Equivalent vs Equal

What are equivalent sets?

• Equivalent sets are sets that have the same cardinality.

• Equivalent sets are sets that contain the same elements.

• Equivalent sets are sets that are subsets of each other.

• Equivalent sets are sets that have different cardinalities.

What are equal sets?

• Sets that contain different elements.

• Equal sets are sets that have the same elements.

• Sets that are subsets of each other.

• Sets that have the same number of elements but different items.

Identify if the sets {1, 2, 3} and {3, 2, 1} are equal or equivalent.

• Equal

• Subset

• Neither

• Equivalent

Are the sets {a, b, c} and {a, b, c, d} equivalent?

• Yes

• They are identical

• No

• {a, b, c, d} is a subset of {a, b, c}

If set A = {x | x is an even number} and set B = {2, 4, 6}, are they equal or equivalent?

• Equal but not equivalent

• Both equal and equivalent

• Neither equal nor equivalent

• Equivalent but not equal

Determine if the sets {1, 2, 3} and {1, 2, 3, 4} are equal or equivalent.

• The sets are both equal and equivalent.

• The sets are equal.

• The sets are equivalent.

• The sets are neither equal nor equivalent.

Can two sets be equivalent if they have different elements?

• Yes, two sets can be equivalent if they have the same number of elements.

• Two sets are equivalent only if they contain identical elements.

• Two sets cannot be equivalent if they have the same number of elements.

• Two sets can only be equivalent if they are both empty.

If set X = {1, 2} and set Y = {2, 1}, are they equal?

• No, set X and set Y are different.

• Yes, set X and set Y are equal.

• No, set Y contains an extra element.

• Yes, set X is a subset of set Y.

What is the difference between equal sets and equivalent sets?

• Equal sets can have different numbers of elements; equivalent sets must have the same elements.

• Equal sets are always larger than equivalent sets.

• Equal sets contain the same elements; equivalent sets have the same number of elements but may differ.

• Equal sets are subsets of each other; equivalent sets are disjoint.

If set P = {a, b} and set Q = {b, a}, are they equal or equivalent?

• Equivalent

• Subset

• Neither

• Equal