. Prove that an→L = Jan] → |L]. (Make cas

Q: Show that R2 =

A: Then, V =Span(S), if every vector in V can be written as a linear combination of elements of S.

Q: 1. f¹ B-A. 2. f is bijective. Suppose f: A→ B. Prove that the following statements are equivalent.

A: A bijection, also known as a bijective function, one-to-one correspondence, or invertible function,…

Q: (9) Let f: A → B, g: B → C and h: C → D. Prove that if hogof: A→D is bijective, then f must be…

A:

Q: Suppose that the translation T is described by (?,?)→(?+2,?−1)(x,y)→(x+2,y−1). What translation…

A: We have to find the translation described in x,y→x+2,y-1.

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

A:

Q: Is the relation R, defined on the set of real numbers by xRy if 2x + y = 3. antisymmetric?

A:

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

A:

Q: if it was Nlo11). Prove that F(2) = 1-F(2)

A: Step 1:We know,  F(z)=2π​1​∫−∞z​e2−t2​dt, so F(−z)=2π​1​∫−∞−z​e2−t2​dt. Step 2: By using the…

Q: Let A = {1,2,...,n} and consider the functions f: A → A. a. How many functions satisfy f(1) = 1? b.…

A: This question related to function and bijection.

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: Let c E R and suppose that an → a. Show that can → ca.

A:

Q: Count the number X of functions y: (20, 21,..., 23) → (5,6,...,8) so that is not onto. X =

A: Given function φ:(20,21,...,23)→(5,6,...,8)

Q: If X, Y, Z ER and x≤Z, show that XL Y S z if and only if |x-y| + | y-z| = |x-z). Interpret…

A:

Q: 24.4. Let A = {1, 2} and B = {3, 4). Write down all functions f : A → B. Indicate which are…

A: Given sets are    and                The cardinality of A is   (  Number of elements in A…

Q: Let z = 6ex²y³. Then: дz дх дz ду

A: We can solve this as follows:

Q: Is 1z = 1 for all z ∈ C?

A:

Q: et x + y+ z=5 where x, y, z E R. Prove that x² + y² + z² >

A:

Q: Consider the relation S on N defined by uSy⟺5|(y+u). Is it reflexive?

A: No it is not a reflexive relation

Q: Let  Z∼N(0,1) . Then  P(Z>−0.73)  is     A.) 0.7673     B.) 0.4757     C.) 0.9418     D.) 0.6215

A: Given: Z~N (0,1)

Q: If a € R such that 0 0, then show that a = 0.

A:

Q: 1 Assume that Pr[A]=0.45 Pr[B]=0.65, and Pr[A∩B]=0.25  A. Pr[B Compliment ∩ A]= B. Pr[A Compliment…

A: Given, Pr[A]=0.45 Pr[B]=0.65 Pr[A∩B]=0.25

Q: は F-R m Show that u is 3. sauomphic to F

A: V is isomorphic to F3 means  There is a bijection map between V to F3 such that that bijection is…