{"id":40714,"date":"2024-04-26T23:06:56","date_gmt":"2024-04-26T23:06:56","guid":{"rendered":"http:\/\/localhost\/branding\/substitution-instances\/"},"modified":"2024-04-26T23:06:56","modified_gmt":"2024-04-26T23:06:56","slug":"substitution-instances","status":"publish","type":"post","link":"https:\/\/sheilathewriter.com\/blog\/substitution-instances\/","title":{"rendered":"Substitution Instances"},"content":{"rendered":"<p>Substitution Instances<\/p>\n<p>(1)    a. (1)~(X \u2283 Y) \u2283 ~(P v Q)     it is a Substitution instance ____not a sub. instance <\/p>\n<p>                 (2) ~~(P v Q)<\/p>\n<p>                 (3) ~~ (X \u2283 Y)<\/p>\n<p>          b. (1) ~( F\u2261B) ____Substitution instance it is not a sub. instance <\/p>\n<p>                   (2) Z\u2283 (F\u2261B)<\/p>\n<p>                   (3) ~Z<\/p>\n<p>        c. (1) (X \u2283 Y) \u2283 ~(P v Q)  it is a Substitution instance _____not a sub. Instance  <\/p>\n<p>                 (2) ~~(P v Q)                                 <\/p>\n<p>                 (3) ~ (X \u2283 Y)<\/p>\n<p>        d. (1) ~(P v Q)\u2283 ~Z  ____Substitution instance it is not a sub. Instance  <\/p>\n<p>                 (2) Z_________                                 <\/p>\n<p>                 (3) ~(P v Q)<\/p>\n<p>(2)   a. 1) A \u2283 B   ____Substitution instance it is not a sub. Instance  <\/p>\n<p>                 (2) B \u2283 X__                                 <\/p>\n<p>                 (3) A \u2283 X<\/p>\n<p>        b. (1) ~X \u2283 Y   it is a Substitution instance _____not a sub. Instance  <\/p>\n<p>                 (2) Y\u2283 ~M__                                 <\/p>\n<p>                 (3) ~X \u2283 ~M<\/p>\n<p>        c.  (1) A \u2283 ~ B   ____Substitution instance it is not a sub. Instance  <\/p>\n<p>                 (2) B \u2283 X___                                <\/p>\n<p>                 (3) A \u2283 X<\/p>\n<p>          d.    (1) ( ~ X \u2022 B) \u2283   it is a Substitution instance _____not a sub. Instance  <\/p>\n<p>                 (2) Y \u2283 ~M_                                 <\/p>\n<p>                 (3) ~ ( ~ X \u2022 B) \u2283 M  <\/p>\n<p>(3)  a.  (1) ~ Z v A   it is a Substitution instance _____not a sub. Instance  <\/p>\n<p>                 (2) ~Z_________                                 <\/p>\n<p>                 (3) A <\/p>\n<p>         b.    1) ~(Z \u2261 B) v ~ (A v B)   it is a Substitution instance _____not a sub. Instance  <\/p>\n<p>                 (2) ~~ (Z\u2261B)_________                                 <\/p>\n<p>                 (3) ~(A v B)<\/p>\n<p>      c.    (1) Z v A   ____Substitution instance   it is not a sub. Instance  <\/p>\n<p>                 (2) ~~Z_________                                 <\/p>\n<p>                 (3) A <\/p>\n<p>          d.    1) (Z \u2261 B) v (A v B)   ____Substitution instance it is not a sub. Instance  <\/p>\n<p>                 (2) ~(Z\u2261B)_________                                 <\/p>\n<p>                 (3) ~(A v B)<\/p>\n<p>(4)   a. (1) ~P v X              it is a Substitution instance ______not a sub. Instance <\/p>\n<p>               (2) ~P \u2283 (B \u2022 F)<\/p>\n<p>               (3)Z \u2283 ~ (B \u2022 F)<\/p>\n<p>               (4) ~ (B \u2022 F)         <\/p>\n<p> b.          (1) ~(P v X)              it is a Substitution instance ______not a sub. Instance <\/p>\n<p>               (2) ~P \u2283 (B \u2022 F)<\/p>\n<p>               (3) ~ Z \u2283 (B \u2022 F)<\/p>\n<p>               (4) (B \u2022 F)         <\/p>\n<p>c.            (1) ~P v Z               it is a Substitution instance ______not a sub. Instance <\/p>\n<p>               (2) ~P \u2283 ~ (B \u2022 F)<\/p>\n<p>               (3) Z \u2283 ~ (B \u2022 F)<\/p>\n<p>               (4) ~ (B \u2022 F)    <\/p>\n<p>d.            (1) (P v Z)              ______Substitution instance it is not a sub. Instance <\/p>\n<p>               (2) P \u2283 (B v F)<\/p>\n<p>               (3) Z \u2283 (B \u2022 F)<\/p>\n<p>               (4) (B \u2022 F)    <\/p>\n<p>(5) a.     (1) ~ (P \u2283 Z)              ______Substitution instance it is not a sub. Instance <\/p>\n<p>               (2) ~P v (B v F)<\/p>\n<p>               (3) (B v F) \u2283 Y<\/p>\n<p>               (4) (X v Y)    <\/p>\n<p>      b.      (1)~ (P \u2283 ~X)              ______Substitution instance it is not a sub. Instance <\/p>\n<p>               (2) (B v F) \u2283 ~Y <\/p>\n<p>               (3) ~ P v (B v F)<\/p>\n<p>               (4) ~ (X v Y)    <\/p>\n<p>      c.       1) (P \u2022 X)              it is a Substitution instance ______not a sub. Instance <\/p>\n<p>               (2) P\u2283 X <\/p>\n<p>               (3) Q \u2283 Y <\/p>\n<p>               (4) X v Y    <\/p>\n<p>      d.     1)~ P \u2283 ~X              ______Substitution instance it is not a sub. Instance <\/p>\n<p>               (2) (B v F) \u2283 ~Y <\/p>\n<p>               (3) ~ P v (B v F)<\/p>\n<p>               (4) ~ X v Y<\/p>\n<p>6.           a.   1)~ P \u2022 Z               it is a Substitution instance ______not a sub. Instance<\/p>\n<p>              2) ~ P<\/p>\n<p>       b.     1)  ~(P \u2022 Q) \u2022 R   ______Substitution instance it is not a sub. Instance<\/p>\n<p>            2) ~P \u2022 ~Q<\/p>\n<p>      c.    1)  (~P \u2022 Q) \u2022 Z   it is a Substitution instance ______not a sub. Instance<\/p>\n<p>             2) ~P \u2022 Q<\/p>\n<p>       d.      1)  (P \u2022 Q) \u2022 R   ______Substitution instance it is not a sub. Instance<\/p>\n<p>                2) P <\/p>\n<p>5. Al dislikes Airedales; moreover, Bob likes beagles. <\/p>\n<p>A \u2227 B<\/p>\n<p>6. Darla has a dachshund, yet Catherine has a Catahoula <\/p>\n<p>D \u2022 C <\/p>\n<p>7. Darla has a dachshund and Catherine has a Catahoula <\/p>\n<p>D \u2022 C<\/p>\n<p>8. Darla has a dachshund unless Al dislikes Airedales <\/p>\n<p>D \u2283 ~A<\/p>\n<p>9. Unless Darla has a dachshund, Bob likes beagles <\/p>\n<p>B \u2283 D<\/p>\n<p>10. Bob likes beagles or Al likes Airedales <\/p>\n<p>B v A<\/p>\n<p>11. If Bob likes beagles it is not the case that Al likes Airedales <\/p>\n<p>A \u2283 ~B<\/p>\n<p>12. Al likes Airedales and\/or Darla has a dachshund <\/p>\n<p>A v D <\/p>\n<p>13. Darla has a dachshund is a sufficient condition for Al likes Airedales <\/p>\n<p>D \u2283 A <\/p>\n<p>14. Darla has a dachshund is a necessary condition that Al likes Airedales<\/p>\n<p>  D \u2283 A <\/p>\n<p>15. Bob likes beagles implies that Catherine has a Catahoula <\/p>\n<p>B \u2022 C<\/p>\n<p>16. Bob likes beagles on the condition that Al likes Airedales <\/p>\n<p>B \u2283 A<\/p>\n<p>17. If Bob likes beagles then Bob likes beagles<\/p>\n<p>B \u2283 B <\/p>\n<p>18. Catherine has a Catahoula only if AI likes Airedales<\/p>\n<p>C \u2283 A <\/p>\n<p>19. Darla has a dachshund given Al likes Airedales <\/p>\n<p>D \u2283 A <\/p>\n<p>20. Provided Al likes Airedales, Bob likes beagles<\/p>\n<p>B \u2283 A <\/p>\n<p>21. Catherine has a Catahoula if and only if Bob likes beagles<\/p>\n<p>C \u2283 C <\/p>\n<p>22. Bob likes beagles if Darla has a dachshund <\/p>\n<p>B \u2283 D<\/p>\n<p>23. Al likes Airedales or Bob doesn\u2019t like beagles<\/p>\n<p>A v ~B <\/p>\n<p>24. Al likes Airedales or Al doesn\u2019t like Airedales <\/p>\n<p>A v ~A<\/p>\n<p>25. Al likes Airedales just in case Bob doesn\u2019t like beagles<\/p>\n<p>A? ~B<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Substitution Instances (1) a. (1)~(X \u2283 Y) \u2283 ~(P v Q) it is a Substitution instance ____not a sub. instance<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-40714","post","type-post","status-publish","format-standard","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Substitution Instances - sheilathewriter<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sheilathewriter.com\/blog\/substitution-instances\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Substitution Instances - sheilathewriter\" \/>\n<meta property=\"og:description\" content=\"Substitution Instances (1) a. 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