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- "question": "Show that `A nnB = A nnB`implies `A = B`",
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- "question": "Out of 500 car owners investigated, 400 owned car\r\n A and 200 owned car B, 50 owned both A and B cars. Is this data correct?",
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- "question": "A market research group conducted a survey of\r\n 1000 consumers and reported that 720 consumers like product A and 450\r\n consumers like product B. what is the least number that must have liked both\r\n products?",
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- "question": "A college warded 38 medals in football, 15 in\n basketball and 20 in cricket. If these medals went to a total of 58 men and\n only three men got medals in all the three sports, how many received medals\n in exactly two of the three sports?",
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- "ocr_text": "Write the set `{1/2,2/3,3/4,4/5,5/6,6/7}`in the setbuilder form.",
- "question": "Write the set `{1/2,2/3,3/4,4/5,5/6,6/7}`in the setbuilder form.",
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- "question": "State which of the following\r\n sets are finite or infinite :\n(i) `{x\" \":\" \"x in N\" \"a n d\" \"(x\" \"\" \"1)\" \"(x\" \"\" \"2)\" \"=\" \"0}`\n\n(ii) `{x\" \":\" \"x\"\"\"\" in N\" \"a n d\"\"\"\"\"\"x^2=\" \"4}`\n\n(iii) `{x\" \":\" \"x in N\" \"a n d\" \"2x\" \"\" \"1\" \"=\" \"0}`\n\n(iv) `{x\" \":\" \"x ",
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- "ocr_text": "Find the pairs of equal sets, if any, give reasons:`A = {0},` `B= {x : x > 15 a n d x < 5},``C = {x : x 5 = 0 },``D = {x : x^2= 25},``E = {x : x i s a n in t egr a l pos i t i v e ",
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- "ocr_text": " Let `A = {a , e , i , o, u}`and `B = {a , i , u}dot`Show that `AuuB = A`",
- "question": "Let `A\" \"=\" \"{a ,\" \"e ,\" \"i ,\" \"o,\" \"u}`\nand `B\" \"=\" \"{a ,\" \"i ,\" \"u}dot`\nShow that `AuuB\" \"=\" \"Adot`",
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- "question": "Let `A = {2, 4, 6, 8}`and `B = {6, 8, 10 , 12}dot`Find `Auu Bdot`",
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- "question": "Let `A=\" \"{1,2,3,4,5,\" \"6,\" \"7,\" \"8,\" \"9,\" \"10}`\nand `B\" \"=\" \"{\" \"2,3,5,7\" \"}dot`\n\nFind `A nnB`\nand hence show that `A nnB\" \"=\" \"Bdot`",
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- "ocr_text": " Let `V = {a , e , i , o, u}`and `B = {a , i , k , u}`. Find `V - B a n d B - V `",
- "question": "Let `V\" \"=\" \"{a ,\" \"e ,\" \"i ,\" \"o,\" \"u}`\nand `B\" \"=\" \"{a ,\" \"i ,\" \"k ,\" \"u}`\n. Find `V\" \"\" \"B\" \"a n d\" \"B\" \"\" \"V`",
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- "ocr_text": " Let `A = {1, 2, 3, 4, 5, 6}`, `B = {2, 4, 6, 8}`. Find `A - B a n d B - A`.",
- "question": "Let `A\" \"=\" \"{1,\" \"2,\" \"3,\" \"4,\" \"5,\" \"6}`\n, `B\" \"=\" \"{2,\" \"4,\" \"6,\" \"8}`\n. Find `A\" \"\" \"B\" \"a n d\" \"B\" \"\" \"A`\n.",
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- "ocr_text": "Show that the set of letters needed to spell “CATARACT” and the set of letters needed to spell “TRACT” are equal.",
- "question": "Show\r\n that the set of letters needed to spell CATARACT and the set of letters\r\n needed to spell TRACT are equal.",
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- "question_language": "English",
- "ocr_text": "List all the subsets of the set `{1, 0, 1 }dot`",
- "question": "List all the subsets of the set `{1, 0, 1 }dot`",
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- "ocr_text": "In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.",
- "question": "In\r\n a survey of 400 students in a school, 100 were listed as taking apple juice,\r\n 150 as taking orange juice and 75 were listed as taking both apple as well as\r\n orange juice. Find how many students were taking neither apple juice nor\r\n orange juice",
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- "ocr_text": " There are 200 individuals with a skin disorder, 120 had been exposed to the chemical `C_1`? 50 to chemical `C_2`, and 30 to both the chemicals `C_1`and `C_2`. Find the number of individuals exposed to(i) Chemical `C_1`but not chemical `C_2`",
- "question": "There are 200 individuals with a skin disorder,\r\n 120 had been exposed to the chemical `C_1`\n? 50 to chemical `C_2`\n, and 30 to both the chemicals `C_1`\nand `C_2`\n. Find the number of individuals exposed to\n(i)\r\n Chemical `C_1`\nbut\r\n not chemical `C_2`",
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- "question_language": "English",
- "ocr_text": "In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach both physics and mathematics. How many teach physics?",
- "question": "In\r\n a school there are 20 teachers who teach mathematics or physics. Of these, 12\r\n teach mathematics and 4 teach both physics and mathematics. How many teach\r\n physics?",
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- "ocr_text": "In a class of 35 students, 24 like to play cricket and 16 like to play football. Also, each student likes to play at least one of the two games. How many students like to play both cricket and football?",
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- "ocr_text": "If X and Y are two sets such that X `uu`Y has 50 elements, X has 28 elements and Y has 32 elements, how many elements does X `nn`Y have?",
- "question": "If X and Y are two sets such that X `uu`Y has 50 elements, X has 28 elements and Y has 32 elements, how many elements does X `nn`Y have?",
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- "question": "Let `U\" \"=\" \"{1,\" \"2,\" \"3,\" \"4,\" \"5,\" \"6,\" \"7,\" \"8,\" \"9,\" \"10}`\nand `A\" \"=\" \"{1,\" \"3,\" \"5,\" \"7,\" \"9}`\n. Find `A^(prime)`\n.",
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