2. a total of 49 internet users visited at least 1 of 3 websites: a news site, a shopping site, and a blog…

Explanation:

Step1: Find users who visited news and shopping and blog.

Let ( N ) be news site, ( S ) be shopping site, ( B ) be blog.
Users who visited ( N ) and ( S ) but not ( B ) is 5, only ( N ) is 8. Total ( N ) visitors: 28.
So users who visited ( N ) and ( S ) and ( B ): Let ( x = |N \cap S \cap B| ).
( |N| = ) only ( N ) ( + ) ( N \cap S ) only ( + ) ( N \cap B ) only ( + x ).
We know only ( N = 8 ), ( N \cap S ) only ( = 5 ). Let ( y = |N \cap B| ) only.
( 28 = 8 + 5 + y + x ) → ( y + x = 15 ). But we'll use another approach.

Step2: Find users who visited news and blog only.

First, users who visited ( N ) and ( S ) (including ( B )): ( N \cap S ) is 5 (only ( N \cap S )) ( + x ) (all three).
But total ( N ) visitors: only ( N ) (8) + ( N \cap S ) only (5) + ( N \cap B ) only + ( x ) = 28.
So ( N \cap B ) only ( + x = 28 - 8 - 5 = 15 ).

Step3: Find users who visited all three (x).

Total users: 49. Let's denote:

• Only ( N ): 8
• ( N \cap S ) only: 5
• ( S \cap B ) only: 4
• Only ( S ): let ( z )
• Only ( B ): let ( w ) (what we need)
• ( N \cap B ) only: let ( y )
• ( x ): all three.

Total: ( 8 + 5 + z + 4 + y + x + w = 49 ).

Also, ( S ) visitors: 31 = only ( S ) + ( N \cap S ) only (5) + ( S \cap B ) only (4) + ( x ).
So ( z + 5 + 4 + x = 31 ) → ( z + x = 22 ).

Step4: Use total users to find remaining.

Total users: ( 8 + 5 + z + 4 + y + x + w = 49 ).
We know ( B ) visitors: 26 = only ( B ) + ( N \cap B ) only + ( S \cap B ) only + ( x ) → ( w + y + 4 + x = 26 ) → ( w + y + x = 22 ).

From ( N ) visitors: ( 8 + 5 + y + x = 28 ) → ( y + x = 15 ). So ( w + 15 = 22 ) → ( w = 7 )? Wait, no, let's correct.

Wait, total users:
Only ( N ) (8) + ( N \cap S ) only (5) + Only ( S ) (z) + ( S \cap B ) only (4) + Only ( B ) (w) + ( N \cap B ) only (y) + ( x ) (all three) = 49.

From ( S ) visitors: ( z + 5 + 4 + x = 31 ) → ( z + x = 22 ) → ( z = 22 - x ).

From ( N ) visitors: ( 8 + 5 + y + x = 28 ) → ( y + x = 15 ) → ( y = 15 - x ).

From ( B ) visitors: ( w + y + 4 + x = 26 ) → ( w + (15 - x) + 4 + x = 26 ) → ( w + 19 = 26 ) → ( w = 7 )? Wait, no, that can't be. Wait, let's use Venn diagram.

Alternative approach:

Let’s define the regions:

1. Only News (N): 8
2. News and Shopping only (N∩S only): 5
3. Shopping and Blog only (S∩B only): 4
4. News, Shopping, Blog (N∩S∩B): x
5. News and Blog only (N∩B only): let’s call this a
6. Only Shopping (S only): b
7. Only Blog (B only): c (what we need)

Total users: 8 + 5 + b + 4 + a + x + c = 49 → 17 + b + a + x + c = 49 → b + a + x + c = 32.

News visitors: 8 (only N) + 5 (N∩S only) + a (N∩B only) + x (all three) = 28 → 13 + a + x = 28 → a + x = 15. (Equation 1)

Shopping visitors: b (only S) + 5 (N∩S only) + 4 (S∩B only) + x (all three) = 31 → b + 9 + x = 31 → b + x = 22. (Equation 2)

Blog visitors: c (only B) + a (N∩B only) + 4 (S∩B only) + x (all three) = 26 → c + a + 4 + x = 26 → c + a + x = 22. (Equation 3)

From Equation 1: a = 15 - x. Substitute into Equation 3: c + (15 - x) + x = 22 → c + 15 = 22 → c = 7. Wait, but let's check total users.

From Equation 2: b = 22 - x.

Now, total users: 8 + 5 + (22 - x) + 4 + (15 - x) + x + 7 = 8 + 5 + 22 - x + 4 + 15 - x + x + 7 = (8+5+22+4+15+7) - x = 61 - x = 49 → x = 12.

Then a = 15 - 12 = 3, b = 22 - 12 = 10.

Check blog visitors: c (7) + a (3) + 4 + x (12) = 7 + 3 + 4 + 12 = 26. Correct.

Check total users: 8 + 5 + 10 + 4 + 3 + 12 + 7 = 49. Correct.

So only blog is 7? Wait, no, wait: when x=12, a=3, b=10, c=7. Let's verify news visitors: 8 (only N) + 5 (N∩S only) + 3 (N∩B only) + 12 (all three) = 28. Correct. Shopping visitors: 10 (only S) + 5 (N∩S only) + 4 (S∩B only) + 12 (all three) = 31. Correct. Blog visitors: 7 (only B) + 3 (N∩B only) + 4 (S∩B only) + 12 (all three) = 26. Correct. Total users: 8+5+10+4+3+12+7=49. Correct.

Wait, but earlier I thought maybe 7, but let's recheck.

Wait, the key step: from total users, we have 8 (only N) + 5 (N∩S only) + 4 (S∩B only) + x (all three) + a (N∩B only) + b (only S) + c (only B) = 49.

We found that a + x = 15 (from N visitors), and c + a + x = 22 (from B visitors). So c = 22 - 15 = 7. Yes, that's a simpler way. Since a + x is 15 (from N's total), then c + 15 + 4 = 26? Wait no, B's total is c (only B) + a (N∩B only) + 4 (S∩B only) + x (all three) = 26. So c + (a + x) + 4 = 26. Since a + x = 15, then c + 15 + 4 = 26 → c = 26 - 19 = 7. Yes, that's correct.

So the number of users who visited only the blog is 7.

Answer:

7