Is {2,2}={2, {2} }? How many elements are in the set {a,a,a,a,a}? {x€N|xis greater than 10 and x is divisible by 3} {x€Z|x is prime and x is divisible by 2} {X c is eqaul to z| x squared = 4}

Q: 4. How many subsets are there of {1, 2, 3, 4, 5}? How many contain at least three elements? How many…

A: Given set is S=1,2,3,4,5 Since we know that, if a set contains n elements, then total number of…

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Q: Let n>,2 and k be any boretine Proce that integers (n-1)* | n, 2

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Q: 2.3 How many integers between 0 and 500: 1. Have distinct digits? 2. Are divisible by 3? 3. Are…

A: Formulae used: Total number of elements in the events E1 or E2 : n(E1∪E2)=n(E1)+n(E2)-n(E1∩E2) Total…

Q: [Q1] From the letters {A, B, C, D, E, F, G}, how many: (a) 3-distinct-letters codes can be…

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Q: 3. Let z and y be 3-digit numbers such that y is equal to r written backwards. For example, if x =…

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Q: 14. Let A, be the set of all multiples of 2 except for 2. Let Az be the set of all multiples of 3…

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Q: What are the values for x1, x2 and x3? O x1-500 ; x2-57.78, x3-175.56 O x1-500; x2=-175.56, x3-57.78…

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Q: How may elements are in the set [-2, 2] \N?

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Q: Let $n$ be a positive integer. Among C(2n,0),C(2n,1),..., C(2n,2n), C(2n,n) is the largest. True…

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Q: How many ways can the letters of the word MAILBOX be arranged in a row so that  M and A Not…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: -, 1+2+2 '+.+ 2 -1 for all natural numbers n.

A: We will use the principle of mathematical induction to prove the result.

Q: p + 2 is a prime number, prove that p2+3 is divisible by 4. (2.5

A: Prime and divisibility

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Q: Given 10 numbers a1, a2,.… , a10, from the set S natural numbers S = {1,2,3, ., 100} . Prove that…

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Q: Prove that if for some integers a, b, c we have that a° + 6° + c° is divisible by 9, thên at least…

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Q: In how many distinct ways can the digits in the number 1,238,229,168 be arranged?

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Q: 2. Let, a, = 3, az = 4 and for n 2 3, a, = 2a,-1 + an-2+ 5, express a, in terms of n.

A: Topic:- series sum

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Q: Assume that A={A,B,C} and B={5,4,1,9,6} A code consists of 2 different symbols selected from X…

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Q: How many elements are there in the greatest conjugacy class of 5 ?S

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Q: How many subsets are there of the set N = {5, 42}?

A: We ahave to find no. Of subsets.

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Q: 2. Prove that n = aŋɑp-1 aza,a, is divisible by 8 if and only if aza,a, is divisible by 8. A…

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Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1 +an-2 +n², express an in terms of n. %3D

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Q: 2. Show that if a]b then a'|b² for all integers a and b (Symbols V, 3, A, V, V,A,→,-)

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Q: 17) How many elements are in the union of four sets if the sets have 100, 150, 250, and 400…

A: Here, n(A)= 100, n(B), 150, n(C)=250, n(D)=400 n(A∩B)=15, n(A∩C)=15, n(A∩D)=15, n(B∩C)=15,…

Q: How many subsets are there of the set N = {6, 49}?

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Q: [Q1] From the letters {A, B, C, D, E, F, G}, how many: (a) 3-distinct-letters co can be generated?…

A: Given: There are 7 letters A, B, C, D, E, F, G

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Q: 1. How many 3-digit numbers can be forms from the four digits 0,1,2,3 if: a) no two digits are to be…

A: according to our guidelines we can answer only three subparts, or any question and rest can be…

Q: 1..Find the number of words of length 7 using letters from {A,B,C,D,E,F} in which no two consecutive…

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Q: Prove that a natural number (an-1an-2a1ao)10 is divisible by 9 if and only if the sum of the digits…

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Q: Let A denote the set of all 4 digit numbers that are divisible by 3, and B denote the set of all 4…

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Q: How many 5-tuples (x1, x2, x3, x4, X5) of positive integers from 1 to n are there? How many 5-tuples…

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Q: 3. Let z and y be 3-digit numbers such that y is equal to x written backwards. For example, if x =…

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Q: Two numbers a and b are chosen from the set 1,2,.., 3n In how many ways can these integers be…

A: In the question we have to find total no. of cases by which a2-b2 is divisible by 3.

Q: Let p, q, and r be primes other than 3. Show that 3 divides p2 + q2 + r2.

A: We have to prove that 3 divides p2+q2+r2, where p,q and r primes other than 3.

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