Consider this statement: "If there is life on Mars, then there has to be water on Mars." Assume that this a TRUE statement. Now answer the following. a) Write the above statement as a sufficient condition. b) Write the above statement as a necessary condition. c) Write the contrapositive of this statement. d) Write the above statement as an "only if" statement. e) Is it possible to write the above statement in "if and only if" form? f) If there is water on Mars, does it mean that there exists life on Mars? Explain.

Consider this statement: "If there is life on Mars, then there has to be water on Mars." Assume that this a TRUE statement. Now answer the following. a) Write the above statement as a sufficient condition. b) Write the above statement as a necessary condition. c) Write the contrapositive of this statement. d) Write the above statement as an "only if" statement. e) Is it possible to write the above statement in "if and only if" form? f) If there is water on Mars, does it mean that there exists life on Mars? Explain.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Consider this statement: "If there is life on Mars, then there has to
be water on Mars." Assume that this a TRUE statement. Now answer
the following.
a) Write the above statement as a sufficient condition.
b) Write the above statement as a necessary condition.
c) Write the contrapositive of this statement.
d) Write the above statement as an "only if" statement.
e) Is it possible to write the above statement in "if and only if" form?
f) If there is water on Mars, does it mean that there exists life on Mars?
Explain.

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