## Classical Banach spaces I and II by Joram Lindenstrauss, Lior Tzafriri

By Joram Lindenstrauss, Lior Tzafriri

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E. y-x. 9 shows that the theorem and its contraposidve theorem have the same set of truth values and the converse theorem has the same set of truth values as the inverse theorem. 9 It follows therefore that it may be possible to take advantage of this result if the contrapositive form of a theorem is easier to prove than the theorem itself, and we should consider the next example with this in mind. Example 21. Given that η is a positive integer prove that if Solution. Just to identify the foregoing remarks we suggest is odd then Η is odd.

Discuss the validity of the following argument: The kitchen is the most dangerous room in the home, therefore it would be safer to cook in the bedroom. SWITCHING CIRCUITS A simple switch is represented by the type of diagram in Fig. 1, in which the switch is used to interrupt current flowing between Ρ and Q. The two-state on-off form of switch enables it to register the true-false nature of a statement. This allows us to refer to the statement and the switch by the same letter symbol. I ^ 1 Fig.

6 Say whether the following conditionals are true or false: 1. If 6 X 4 = 24 then 6 χ 8 = 48. 2. If 6 X 4 = 25 then 6 X 8 = 50. 3. Ifx = 5then4x = 20. 4. If 4 is a prime number then 4 + 3 = 7. 5. If London is in France then Paris is in England. 6. If New York is in the USA then Paris is in Australia. 7. If sets A, Β are disjoint (T) then AnB = AuB. 8. If X # 0 and X < 0 then χ > 0. 9. For a quadrilateral to be a square it is sufficient that all of the angles be right-angles. 10. A necessary condition for a quadrilateral to be a square is that all its sides be of equal length.