Prove that if A∩B=0, then P(A∪B)=P(A)×P(B), where P(x) denotes the power set of x.Here’s the best way to solve it. Solution Share Step 1 A∩B=0 i...View the full answer Step 2 Unlock Step 3 Unlock Step 4 Unlock Step 5 Unlo...
【解析】 By definition, the cross product of two vectors a*b=|ab|sin(θ) , where is the angle between a a nd . and n is a unit vector normal (perpendic ulan) to the plane containing a and b. So if a, b, c and a are all on the same plane, both āxb and ēxd will b...
-ata=0 Reason: Axiom (AI): additive inverse 5. 0+b=0+c Reason: Equation substitution 6. b=c Reason: Axiom (Z): zero Below is a translation of the above stepwise proof into English sentences. Proof. If a +b = a + c then -a...
(b) (i)(A∩B)⊂A (ii)(A∩B)⊂B. View Solution View Solution Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar...
Prove that if A is invertible and AB = O, then B = O. If A^2 = 0, prove that A cannot be invertible. Let A be invertible. Prove that A^T is invertible and (A^T)^{-1} = (A^{-1})^T. Let A and B be n ...
Let a, b, an d c be integers. Prove the following:1. If b+ a =c+a, then b= c.2. For each integer a, a.0=0.3. For each integer a, -(-a)= a.4. a⋅(-b)=-(ab) .5. (-a)⋅(-b)=a⋅ b .6.-(a+b)=(-a)+(-b).7. Prove that if a + b= a, ...
Answer to: Prove that if P(AB) = P(A) P(B), then P(A|B) = P(A). By signing up, you'll get thousands of step-by-step solutions to your homework...
35. (a) Prove that if A and B are symmetric n × n matrices,then so is A + B.(b)Prove that if A is a symmetric n × n matrix, then so is k A for any scalar k. 相关知识点: 试题来源: 解析 ∴(A+B)^T=A+B^T=A+B (b) (kA)^T=kA^T=kA ...
两种情况都有可能。1.有理数 例如：a=2，b=3，则a的b次方=8 2.无理数 例如：a=3，b=1/2，则a的b次方=根号3 综上，可得：当b为整数时，a的b次方是有理数；b为分数时，a的b次方可能是无理数（前提是a的b次方要有意义）
Answer to: Prove that if a|b and a|c, then a|(b + c), where a, b, and c are natural numbers. By signing up, you'll get thousands of step-by-step...