MATH1061/7861, Wed 12 Aug 2020 Predicates: sentences with “free variables” whose values are not yet known
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Question 1. Determine whether or not the following argument is valid:
If new messages are queued, then the filesystem is locked.
The filesystem is not locked if and only if the system is functioning normally. New messages will not be sent to the message buffer only if they are queued. New messages will not be sent to the message buffer.
Hence the system is not functioning normally.
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the premises true but the conclusion false.
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n functioning normally Decide whether it is valid using three methods: (a) truth tables; (b) rules of inference; and (c) find truth values that would make
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Question 2. Translate the following English sentences into formal quantified statements, and determine whether they are true
or false:
A. There is a real number that is also an integer. Fx EIR such that x C 2 TRUE
B. If a real number is an integer, then it is a rational number. eI xtQM D. 7
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Question 3. Translate the following formal quantified statements into English sentences, and determine whether they are true
orfalse:
Thereexistsa realnumber x such that x2 2 TRUE x FL
A. All prime numbers are odd.
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A. If an integer is divisible by 2 then it is divisible by 4.
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A. ∃x∈Rsuchthatx2=2.
B. ∀x ∈ {1, 2, 3, 4, 5}, x is prime.
C. ∃x∈{1,2,3,4,5}suchthatx>4. F te fhz D. ∀x ∈ R, if x3 < 8 then x < 2.
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