a) V.VXA-o, b) VX V-D-O マ×(マ×ズ)= マ(アオ)ー ブイ )v(ズx2)=でしマメズ)ーオ(マ×ご) %3D

Q: Prove that A u (B n C) = (Au B) n (A u C).

A:

Q: 50000 00012. [8] 2 [+] 剧 的条目 72 = 2 元 dx 衙路2跨小嶝小鸡小 1000 1

A:

Q: Is the following true or false? Z∩N=Z

A: Z is the set of all integers, i.e.  Z={ ..., -3, -2, -1, 0, 1, 2, 3, ...} And N is the set of all…

Q: Prove that z =z iff z is real.

A: z represents a complex number which is in the form x+iy, where x and y are the real numbers and i is…

Q: ZW and ZX are supplementary and ZW and ZY are supplementary. Construct a proof that ZX = ZY.

A: <W  and < X  are supplementary angle  the sum of supplementary angles = 180 degree <W  and…

Q: Are u sure its not 1

A: It is given that a=0 and b=1.

Q: Let x, y EZ. Prove that 3|xy if and only if 3|x x or 3 y.

A:

Q: Prove that for all a, b, and c e Z, if a † (2bc+12), then a † (b – 2) or a ł (c + 3).

A:

Q: Prove that if CE AB and C+ A, then AB AĆ.

A:

Q: Let a < b be real numbers, and let T Qn [a, b]. Prove that sup T = b. =

A:

Q: 1-a*** a zi i. La 1-a

A:

Q: Prove.

A:

Q: Let r ERQ. Prove that for all a, b, c EQ, =cr iff a = 0 and b = c. a + br

A: Given that r∈RQ Let a,b,c∈Qa+br=cr iff a=0 and b=c

Q: If A and B are independent, prove that B and the complement of A are independent.

A: Given,A and B are independent events , so P(A∩B)=P(A)×P(B) .

Q: Let a, b, c € Z with c‡0. Prove that if a | b, then ac | be

A: Let a,b,c∈Z and c≠0. Let ab. Then b=ak, for some integer k.

Q: Show that if AB = I, then det(A) 0 and det(B) # 0.

A: Here given as AB=In find determinant both sides detAB=detIndetAB=1

Q: Suppose that a divides b and that c divides b. Suppose that gcd(a, c) = 1. Prove that ac divides b.

A:

Q: 14. Prove that AC B if and only if An BC= 0.

A: The objective is to prove the above question.

Q: Prove that ||A||1 = max1<j<n{£", |aij|}. %3D

A:

Q: Prove that if ACØ then A = (Ø.

A: To prove the given statement.

Q: 3. Prove that if a 0.

A: To prove that if a&lt;0 and b&lt;0, then ab&gt;0.

Q: Theorem 4 If B CA, P(B)< P(A).

A:

Q: if| A - B | = | A + B | . prove that A is orthogonal on B

A: Given, A-B=A+B

Q: If x > 0, prove that T - In (1+ x) > 2+2x

A: Using derivative

Q: (1-exjdy of 28 on Find the halutiom

A:

Q: Suppose gcd(ab,c)=1. Prove that abc | d if, and only if ab | d and c | d.

A:

Q: Prove: Provided it exists, (A-1)¯ = A.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Prove that:  If 0 ≠ p ∈ Q and x ∉ Q, then (show that) a + x ∉ Q and ax ∉ q.

A: Given: Let a∈ℚ and x∉ℚ To show: a+x∉ℚax∉ℚ

Q: Let S := a + √2 b + √2 : a, b EN Prove that S is countably infinite.

A: To prove that the set S defined as S={a+2b+2|a,b∈N} is countably infinite, need to establish a…

Q: Let fo find t

A:

Q: Prove that if a < 1 and [b] < 1. a -b = 201₁ āb 1 <1

A:

Q: Let x ∈ R. Prove that if x 0.

A: Given :

Q: Prove that X and Y are independent if and only if R = 0

A: To prove that if x and y are independent then correlation between them R =0

Q: Prove: For c &gt;= 0 , | a | &lt;= c if and only if -c &lt;= a &lt;= c

A: