# unit1 - Hardegree Intermediate Logic Unit 1 Translations in...

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Hardegree, Intermediate Logic ; Unit 1: Translations in Function Logic 1 of 8 UNIT 1: TRANSLATIONS IN FUNCTION LOGIC 1. Directions for all Exercise Sets in Unit 1 Using the suggested abbreviations (the capitalized words), translate each of the following into the language of function logic. Symbolize all and only capitalized words. Important: Write down your lexicon. In each case, clearly indicate what each predicate letter, each function letter, and each proper-noun letter symbolizes. Examples: V [ α ] : α is a voter R [ α , β ] : α respects β S [ α , β , γ ] : α sold β to γ m ( α ) : the mother of α f ( α ) : α ’s father s ( α , β ) : the sum of α and β p ( α , β ) : α plus β j : Jay In writing down the lexicon, use lower case Greek letters as generic arguments (place holders); in particular, use ‘ α ’ for one-place functors, ‘ α ’, ‘ β ’ for two-place functors, and ‘ α ’,‘ β ’,‘ γ ’ for three-place functors. [brief note on Greek alphabet: α is alpha, β is beta, γ is gamma, δ is delta; and, of course, the word ‘alphabet’ comes from ‘ αβ ’] Also, in quantified sentences, identify the universe of discourse (the domain over which the quantifiers range) . For example, U : things (the most general domain) U : persons U : numbers etc. Alternatively, you may write: 2200 x : every thing 2200 x : every person 2200 x : every number etc. Final Note : You may use numerals (‘1’, ‘2’, etc.) to symbolize themselves.

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Hardegree, Intermediate Logic ; Unit 1: Translations in Function Logic 2 of 8 2. EXERCISE SET A 1. JAY's MOTHER is TALL. 2. The SQUARE of TWO is EVEN. 3. The square ROOT of 2 is not RATIONAL. 4. The FIRST bar of JAY's favorite SONG is not MEMORABLE. 5. JAY'S FAVORITE song is LOUDER than KAY'S FAVORITE song. 6. The SQUARE of TWO PLUS FOUR is EVEN (symbolize both readings). 7. The PRODUCT of 3 and 4 is LARGER than the SUM of 3 and 4. 8. JAY'S MOTHER is TALLER than KAY'S FATHER. 9. JAY'S MIDDLE name is the SAME as the FIRST name of the PRESIDENT of the US. 10. ( a + b ) % c = ( a % c ) + ( b % c ). 11. a + b is less than a % b 12. ( a + b ) 2 = a 2 + (2( ab ) + b 2 ). 13. Both of JAY's parents are DEMOCRATS. 14. Neither of KAY's parents is a DEMOCRAT. 15. JAY's parents aren't both POLITICIANS. 16. Exactly one of KAY's parents is a POLITICIAN. 17. At least one of JAY'S parents is an POLITICIAN 18. The sQUARE root of the SUM of 2 and 4 is not RATIONAL. 19. JAY's FATHER is neither HEAVIER nor TALLER than JAY's MOTHER. 20. CAIN did not CLAIM to be his BROTHER's KEEPER.
Hardegree, Intermediate Logic ; Unit 1: Translations in Function Logic 3 of 8 3. EXERCISE SET B 21. Every WOMAN RESPECTS her MOTHER. 22.

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unit1 - Hardegree Intermediate Logic Unit 1 Translations in...

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