A survey of 116 high school students determined whether they used​ Instagram, Twitter, or Facebook. The provided information was determined. 71 used Instagram. 54 used Twitter. 75 used Facebook. 36 used Instagram and Twitter. 45 used Instagram and Facebook. 36 used Twitter and Facebook. 24 had all three features. How many of the students used Instagram or Twitter, but not Facebook?

Let's define the sets: A = The set of students who used Instagram. B = The set of students who used Twitter. C = The set of students who used Facebook. Now, we have the following information: |A| = 71 (the number of students who used Instagram). |B| = 54 (the number of students who used Twitter). |C| = 75 (the number of students who used Facebook). |A ∩ B| = 36 (the number of students who used both Instagram and Twitter). |A ∩ C| = 45 (the number of students who used both Instagram and Facebook). |B ∩ C| = 36 (the number of students who used both Twitter and Facebook). |A ∩ B ∩ C| = 24 (the number of students who used all three platforms). We want to find out how many students used Instagram or Twitter but not Facebook. This can be calculated using the principle of inclusion-exclusion: |A ∪ B - (A ∩ C ∪ B ∩ C)| Now, let's calculate the values: |A ∪ B| = |A| + |B| - |A ∩ B| = 71 + 54 - 36 = 89 |A ∩ C ∪ B ∩ C| = |A ∩ C| + |B ∩ C| - |A ∩ B ∩ C| = 45 + 36 - 24 = 57 Now, we can calculate the desired value: |A ∪ B - (A ∩ C ∪ B ∩ C)| = |A ∪ B| - |A ∩ C ∪ B ∩ C| = 89 - 57 = 32 So, 32 of the students used Instagram or Twitter but not Facebook.