Let S be the statement: For all positive real number r and s , r + s ≠ r + s . Statement S is true, but the following “proof” is incorrect. Find the mistake. “Proof by contradiction: Suppose not. That is, suppose that for all positive real numbers r and s , r + s = r + s . This means that the equation will be true no matter what positive real numbers are substituted for r and s . So let r = 9 and s = 16. Then r and s are positive real numbers and r + s = 9 + 16 = 25 = 5 whereas r + s = 9 + 16 = 3 + 4 = 7. Since 5 ≠ 7 , we have that r + s ≠ r + s , which contradicts the supposition that r + s = r + s . This contradiction shows that the supposition is false, and hence statement S is true.”
Let S be the statement: For all positive real number r and s , r + s ≠ r + s . Statement S is true, but the following “proof” is incorrect. Find the mistake. “Proof by contradiction: Suppose not. That is, suppose that for all positive real numbers r and s , r + s = r + s . This means that the equation will be true no matter what positive real numbers are substituted for r and s . So let r = 9 and s = 16. Then r and s are positive real numbers and r + s = 9 + 16 = 25 = 5 whereas r + s = 9 + 16 = 3 + 4 = 7. Since 5 ≠ 7 , we have that r + s ≠ r + s , which contradicts the supposition that r + s = r + s . This contradiction shows that the supposition is false, and hence statement S is true.”
Let S be the statement: For all positive real number r and s,
r
+
s
≠
r
+
s
.
Statement S is true, but the following “proof” is incorrect. Find the mistake. “Proof by contradiction: Suppose not. That is, suppose that for all positive real numbers r and s,
r
+
s
=
r
+
s
.
This means that the equation will be true no matter what positive real numbers are substituted for r and s. So let
r
=
9
and
s
=
16.
Then r and s are positive real numbers and
r
+
s
=
9
+
16
=
25
=
5
whereas
r
+
s
=
9
+
16
=
3
+
4
=
7.
Since
5
≠
7
,
we have that
r
+
s
≠
r
+
s
,
which contradicts the supposition that
r
+
s
=
r
+
s
.
This contradiction shows that the supposition is false, and hence statement S is true.”
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MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY