Intersection and Union
Distinguish intersection and union of sets in Grade 9 algebra: intersection contains elements in both sets (AND), while union contains all elements in either set (OR), applied to solving compound inequalities.
Key Concepts
Property The intersection of sets $A$ and $B$, $A \cap B$, is the set of elements that are in both $A$ and $B$. The union of $A$ and $B$, $A \cup B$, is the set of all elements that are in $A$ or $B$.
Examples If $A = \{1, 3, 5, 7\}$ and $B = \{5, 7, 9\}$, the intersection is $A \cap B = \{5, 7\}$. If $A = \{1, 3, 5, 7\}$ and $B = \{5, 7, 9\}$, the union is $A \cup B = \{1, 3, 5, 7, 9\}$.
Explanation Intersection is like finding out which friends you and your bestie have in common—it’s the overlap! The symbol $\cap$ even looks like a bridge connecting only what's shared. Union is like combining your entire contact list with your friend's list for a huge party. The $\cup$ symbol is like a giant bowl holding every single person from both lists.
Common Questions
What is the difference between intersection and union of sets?
The intersection (∩) of two sets contains only elements that appear in BOTH sets simultaneously. The union (∪) contains all elements that appear in EITHER set or in both.
How does set intersection relate to AND compound inequalities?
Solving an AND compound inequality means finding values that satisfy both conditions — that is the intersection of both solution sets. For A = {x > 1} and B = {x < 5}, A ∩ B = {1 < x < 5}.
How does set union relate to OR compound inequalities?
Solving an OR compound inequality means finding values that satisfy at least one condition — that is the union of both solution sets. For A = {x < -2} and B = {x > 4}, A ∪ B includes all values less than -2 or greater than 4.