Intersection of sets - practice problems
The intersection of sets, denoted by A ∩ B, is the set containing all elements that belong to both set A and set B simultaneously. If sets have no common elements, their intersection is the empty set (∅) and the sets are called disjoint. The intersection operation is commutative (A ∩ B = B ∩ A), associative ((A ∩ B) ∩ C = A ∩ (B ∩ C)), and distributive with union. Venn diagrams visually represent intersections as overlapping regions. Properties include the subset relationship: A ∩ B ⊆ A and A ∩ B ⊆ B. Intersections are fundamental to probability (joint events), logic (conjunction), database queries (selecting records meeting multiple criteria), and solving systems of equations or inequalities.Number of problems found: 198
- Reading newspaper
40% of the people read newspaper x and 50% read newspaper y, and 10% read both the papers. What percentage of people read neither of the newspapers? - Blue region
Find the area of the blue region on the picture. - Failed in examination
In an examination, 20% of total students failed in history,15% failed in English and 5% of total number of students failed in both subjects. Find the percentage of total number of students who passed in both the subjects. - Two games In a class of 65 students, 30 students play cricket, 20 students play tennis, and 10 students play both games. Then, find the number of students who play neither.
- Test and exam
1100 boys and 700 girls appeared in a test. If 42% of boys and 36% of girls passed, then find the percentage of students who failed. - Two points
M and N are two points on the X-axis and Y-axis, respectively. Point P (3, 2) divides the line segment MN in a ratio of 2:3. Find: (i) the coordinates of M and N (ii) slope of the line MN. - Football and cricket In a school 40% of the students play football and 50% play cricket. If 18% of the students neither play football nor cricket, then find the percentage of the students playing both.
- LS and y-axis intersection In what ratio is the line segment joining P (5, 3) and Q (–5, 3) divided by the y-axis? Also, find the coordinates of the intersection point.
- The well 3 When the health department tested private wells in a county for two impurities commonly found in drinking water, it found that 20% of the wells had neither impurity, 40% had impurity A, and 50% had impurity B. (Obviously, some had both impurities. ) If a
- Two sets 2 If X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements and Y has 32 elements, how many elements does X ⋂ Y have?
- An examination
In an examination 65% students passed in English and 56% in mathematics. And 25% failed in both the subjects. If 414 passed in both the subjects, then find the total number of students. - Richard
Richard is conducting an experiment. Every time he flips a fair two-sided coin, he also rolls a six-sided die. What is the probability that the coin will land on tails and the die will land on an even number? - X intercept Given: 3y+2x=-6 Calculate the X-intercept.
- Library and gym In a town, 7/8 of the population has a library card, and 3/4 has a gym membership. What fraction of the population has either a library card or a gym membership?
- And or logic
If A and B are events with P(A)=0.3, P(A OR B)=0.76, and P(A AND B)=0.04, find P(B). Enter your answer in decimal form, rounded to one place. - Three 241
Three-fifths of the t-shirts in a t-shirt shop are blue. Five-eights of those T-shirts are on sale. One-third of the blue of the blue shirts that are on sale are size medium. What fraction of the shop's blue T-shirts are on sale and size medium? - And - or probability rules Given P(A)=0.4, P(B)=0.56, and P(A and B)=0.274, find the value of P(A or B), rounding, if necessary.
- Exactly 4
Exactly 1/6 of the kids are playing on the playground. Exactly 3/5 of the kids are playing soccer. Jack adds 1/6 + 3/5 to find the total fraction of kids at the park playing on the playground or playing soccer. Is he correct? - Five roommates
Five roommates will move into a house with four bedrooms: one double room and three single rooms. The five roommates propose that they draw names to determine the order in which they pick the bedrooms, assuming that the first three names drawn will choose - Ruben
Ruben owns a restaurant. He likes to keep track of everything customers are buying. His top 3 sellers are sandwiches, salads, and pizza. He knows that 1/3 of his customers buy a sandwich, 1/2 buy a salad, and 1/4 buy a pizza. What fraction of customers bu
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