Please do the five questions. Star rating will be the number of right answers. I

Question

Please do the five questions.

Star rating will be the number of right answers.

If more than 3 wrong, I will not take it as an answer.

If you Include your explanation, it will really help!!

Thanks

Let a set S have just four elements a, b, c and d Assume there is a binary operation * on S such that the the table for (y*x) is the following, where the x comes from the top row. and the y comes from the left most column: Here are some statements: * on S has an identity element: Every element in S has a *-inverse: is commutative: How many of the statements are true for S with *? Assume a set S has exactly four elements a,b,c and d and that there is a binary relation # on S such that the following table shows whether or not y#x, where x comes from the top row and y comes from the leftmost column: Her are some statements about S and #: # Is transitive on S: # is total on S, in other words # is irreflexive on S: S has a #-first element: How many of these statements are true? Consider the following four sentences, where # is a binary relation symbol: If a model satisfies all four sentences then that model must have how many elements: Exactly 3 Infinitely many Exactly 2 Exactly 2 or exactly 3 Exactly 1 Consider the four models: reals with the usual

Explanation / Answer

1) C
2)B
3) C
4)C
5)B

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