Use the sets to finf F union (D intersection E) Let D ={12,15,17}, E={12,14,15,16}, and F={11,13,14,15,17}
First, let's find D intersection E:
D intersection E = {12,15}
Next, let's find F union (D intersection E):
F union (D intersection E) = {11,13,14,15,17} union {12,15} = {11,12,13,14,15,17}
To find the union of F with the intersection of D and E (F ∪ (D ∩ E)), we need to first calculate the intersection of sets D and E, and then take the union of the result with set F.
1. Find the intersection of sets D and E:
- D ∩ E = {x | x ∈ D and x ∈ E}
- D ∩ E = {12, 15} (the values that are common to both sets D and E)
2. Take the union of the intersection (D ∩ E) with set F:
- F ∪ (D ∩ E) = {x | x ∈ F or x ∈ (D ∩ E)}
- F ∪ (D ∩ E) = {11, 13, 14, 15, 17} ∪ {12, 15}
- F ∪ (D ∩ E) = {11, 12, 13, 14, 15, 17} (the values that are in either set F or the intersection of D and E)
Therefore, F union (D intersection E) is {11, 12, 13, 14, 15, 17}.
To find F union (D intersection E), we will follow these steps:
Step 1: Find the intersection of sets D and E.
Step 2: Find the union of set F and the intersection from step 1.
Step 1: Find the intersection of sets D and E.
D = {12, 15, 17}
E = {12, 14, 15, 16}
The intersection of D and E is the subset of elements that are common to both sets. In this case, the intersection is {12, 15}.
Step 2: Find the union of set F and the intersection from step 1.
F = {11, 13, 14, 15, 17}
Intersection of D and E = {12, 15}
The union of F and the intersection is the combination of all elements from both sets, without any duplication.
Therefore, F union (D intersection E) = {11, 12, 13, 14, 15, 17}.