Please Solve

Question

If r and s are the statements

r: Macbeth is the Thane of Cawdor

s: Ruth is the Sultan of Swat

Translate each of the following into English

r-s, (b) s-r, (c) ~r  (d) r v s, (e) r-s
 

Answer 1

Karen,

 

First notice that the 2 statements have nothing to do with each, other than both individuals have titles. Babe Ruth a real person was accorded that "Sultan of Swat" title by the New York media when he played baseball as a Yankee. Macbeth is a character from a Shakespeare play that had a title (Thane of Cawdor) bestowed by the King in that play.  So there is no overlap in a Venn diagram of these 2 statements.  Thus:

 

(a) r-s = r.  Taking away Ruth's title or ignoring Ruth won't have any effect on Macbeth.

(b) s-r = s.  Similarly, taking away Macbeth's title or ignoring Macbeth won't have any effect on Ruth.

(c) -r.  Macbeth is NOT the Thane of Cawdor.

(d) r U s.  Macbeth is or was the Thane of Cawdor AND Ruth is or was the Sultan of Swat. Probably should use "was" since neither person is alive now.

(e) r n s corrected; otherwise (a) as written.  The only thing common to both is they have titles. Otherwise, it is null or empty given they are independent.