How to Fix It: To fix this issue, you’ll have to disable some applications that automatically run on startup. Symptoms: Your PC takes a long time to start up and even freezes up during boot. Reason 1: You Have Too Many Startup Programs

Reason 5: Your Hard Drive Is Low on Space.

Reason 4: Your Antivirus Software Is Extremely Active.

Reason 3: You’re Running Too Many Programs at Once.Reason 2: Corrupted Windows System Files.Reason 1: You Have Too Many Startup Programs.Since we know the number of students in all but region a, we can determine that 21 – 6 – 4 – 3 = 8 students are in region a. This includes students from regions a, b, d, and e. Now, we know that 21 students were taking a SS course. Since 9 students were taking SS and HM, there must be 9 – 3 = 6 students in region b. Similarly, since there are 10 students taking HM and NS, which includes regions e and f, there must be 10 – 3 = 7 students in region f. Since we know there are 3 students in region 3, there must be 7 – 3 = 4 students in region d. Since 7 students were taking a SS and NS course, we know that n( d) + n( e) = 7. How many students are only taking a SS course?Īnswers It might help to look at a Venn diagram. From the given data, we know that there are 3 students in region e and 7 students in region h. The previous example illustrated two important propertiesįifty students were surveyed, and asked if they were taking a social science (SS), humanities (HM) or a natural science (NS) course the next quarter. Since the universal set contains 100% of people and the cardinality of F ⋃ T = 90%, the cardinality of ( F ⋃ T) c must be the other 10%. Now, to find how many people have not used either service, we’re looking for the cardinality of ( F ⋃ T) c. To find the cardinality of F ⋃ T, we can add the cardinality of F and the cardinality of T, then subtract those in intersection that we’ve counted twice. Notice that while the cardinality of F is 70% and the cardinality of T is 40%, the cardinality of F ⋃ T is not simply 70% + 40%, since that would count those who use both services twice.

Let T be the set of all people who have used Twitter, and F be the set of all people who have used Facebook.

How many people have used neither Twitter or Facebook? The results show 40% of those surveyed have used Twitter, 70% have used Facebook, and 20% have used both. A survey asks: 'Which online services have you used in the last month?'

Reason 5 setup only