X7. We know that given any real numbers x1 and x2, if x1x2 = 0, then x1 = 0 or x2 = 0. Since there are two factors, let's call this statement P(2). We assume P(2) is true without proving it. a. Use an inductive idea to carefully explain why given any real numbers x1, X2, and x3, if X1X2X3 = 0, then x1 = 0, x2 = 0, or x3 = 0. Be sure to use only P(2) in your argument. Hint: x7x2x3 = (x,x2)x3, which consists of two factors, x1x2, and x3. b. Use an inductive idea to carefully explain why given any real numbers x1, x2, X3, and x4, if X1X2X3X4 = 0, then x1 = 0, x2 = 0, x3 = 0, or x4 = 0. Be sure to use only P(2) or P(3) in %3D your argument.

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X7. We know that given any real numbers x1 and x2, if x1X2 = 0, then x1 = 0 or x2 = 0. Since there
are two factors, let's call this statement P(2). We assume P(2) is true without proving it.
a. Use an inductive idea to carefully explain why given any real numbers x1, X2, and x3, if
X1X2X3 = 0, then x1 = 0, x2 = 0, or X3 = 0. Be sure to use only P(2) in your argument.
Hint: x,x2x3 = (x1X2)X3, which consists of two factors, x1X2, and x3.
b. Use an inductive idea to carefully explain why given any real numbers x1, x2, X3, and x4, if
X1X2X3X4 = 0, then x1 = 0, x2 = 0, x3 = 0, or x4 = 0. Be sure to use only P(2) or P(3) in
%3D
%3D
your argument.
c. Let P(n) be the statement that given any n real numbers x1, X2, ..., Xn, if x,×2 …· Xn = 0,
then xị = 0 for some i. Use mathematical induction to prove P(n) is true for all n > 2. The
base case does not need to be proven, but at least acknowledge its truth.
%3D
ai duppose hi Xe Az = O. Ther ix x} Xq =0. Since P(2) is true, either
X, le:O or Xz = 0. 1f 81 X =0, thn by Pld) uther ĥi-0 or
つ
Enumeration Packet
Math 252 Quiz 5 Spring 2021
Math 420 Note Packet 2 p1-4
Chapter 8- Mathematical induction
X Chapter 6 - Mathematical Ini
Transcribed Image Text:X7. We know that given any real numbers x1 and x2, if x1X2 = 0, then x1 = 0 or x2 = 0. Since there are two factors, let's call this statement P(2). We assume P(2) is true without proving it. a. Use an inductive idea to carefully explain why given any real numbers x1, X2, and x3, if X1X2X3 = 0, then x1 = 0, x2 = 0, or X3 = 0. Be sure to use only P(2) in your argument. Hint: x,x2x3 = (x1X2)X3, which consists of two factors, x1X2, and x3. b. Use an inductive idea to carefully explain why given any real numbers x1, x2, X3, and x4, if X1X2X3X4 = 0, then x1 = 0, x2 = 0, x3 = 0, or x4 = 0. Be sure to use only P(2) or P(3) in %3D %3D your argument. c. Let P(n) be the statement that given any n real numbers x1, X2, ..., Xn, if x,×2 …· Xn = 0, then xị = 0 for some i. Use mathematical induction to prove P(n) is true for all n > 2. The base case does not need to be proven, but at least acknowledge its truth. %3D ai duppose hi Xe Az = O. Ther ix x} Xq =0. Since P(2) is true, either X, le:O or Xz = 0. 1f 81 X =0, thn by Pld) uther ĥi-0 or つ Enumeration Packet Math 252 Quiz 5 Spring 2021 Math 420 Note Packet 2 p1-4 Chapter 8- Mathematical induction X Chapter 6 - Mathematical Ini
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