₂₅ – ₂₉. ɢɪᴠᴇɴ ᴛʜᴀᴛ; ɢ : ᴀ ɢᴏᴏᴅ ᴄᴏᴜɴᴛʀʏ ᴘʀᴏᴅᴜᴄᴇꜱ ɢᴀʟʟᴀɴᴛ ᴍᴇɴ. ᴅ : ᴛʜᴇʏ ᴀʀᴇ ʀᴇᴀᴅʏ ᴛᴏ ᴅɪᴇ ꜰᴏʀ ᴛʜᴇ ᴄᴀᴜꜱᴇ. ᴋ : ɢᴀʟʟᴀɴᴛ ᴍᴇɴ ᴀʀᴇ ᴘʀᴇᴘᴀʀᴇᴅ ᴛᴏ ᴅᴇꜰᴇɴᴅ. ᴛʀᴀɴꜱʟᴀᴛᴇ ᴛʜᴇ ꜱʏᴍʙᴏʟɪᴄ ʟᴏɢɪᴄ ɪɴᴛᴏ ᴘʀᴏᴘᴏꜱɪᴛɪᴏɴᴀʟ ʟᴏɢɪᴄ. ₂₅. ɢ → ᴅ ∧ ᴋ ₂₆. ᴅ → ~ɢ ₂₇. ~(ɢ ∧ ᴅ) → ᴋ ₂₈. ɢ ∨ ᴋ → ~ᴅ ₂₉.~ᴋ ∨ ᴅ → ~ɢ
₂₅ – ₂₉. ɢɪᴠᴇɴ ᴛʜᴀᴛ; ɢ : ᴀ ɢᴏᴏᴅ ᴄᴏᴜɴᴛʀʏ ᴘʀᴏᴅᴜᴄᴇꜱ ɢᴀʟʟᴀɴᴛ ᴍᴇɴ. ᴅ : ᴛʜᴇʏ ᴀʀᴇ ʀᴇᴀᴅʏ ᴛᴏ ᴅɪᴇ ꜰᴏʀ ᴛʜᴇ ᴄᴀᴜꜱᴇ. ᴋ : ɢᴀʟʟᴀɴᴛ ᴍᴇɴ ᴀʀᴇ ᴘʀᴇᴘᴀʀᴇᴅ ᴛᴏ ᴅᴇꜰᴇɴᴅ. ᴛʀᴀɴꜱʟᴀᴛᴇ ᴛʜᴇ ꜱʏᴍʙᴏʟɪᴄ ʟᴏɢɪᴄ ɪɴᴛᴏ ᴘʀᴏᴘᴏꜱɪᴛɪᴏɴᴀʟ ʟᴏɢɪᴄ. ₂₅. ɢ → ᴅ ∧ ᴋ ₂₆. ᴅ → ~ɢ ₂₇. ~(ɢ ∧ ᴅ) → ᴋ ₂₈. ɢ ∨ ᴋ → ~ᴅ ₂₉.~ᴋ ∨ ᴅ → ~ɢ
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
₂₅ – ₂₉. ɢɪᴠᴇɴ ᴛʜᴀᴛ;
ɢ : ᴀ ɢᴏᴏᴅ ᴄᴏᴜɴᴛʀʏ ᴘʀᴏᴅᴜᴄᴇꜱ ɢᴀʟʟᴀɴᴛ ᴍᴇɴ.
ᴅ : ᴛʜᴇʏ ᴀʀᴇ ʀᴇᴀᴅʏ ᴛᴏ ᴅɪᴇ ꜰᴏʀ ᴛʜᴇ ᴄᴀᴜꜱᴇ.
ᴋ : ɢᴀʟʟᴀɴᴛ ᴍᴇɴ ᴀʀᴇ ᴘʀᴇᴘᴀʀᴇᴅ ᴛᴏ ᴅᴇꜰᴇɴᴅ.
ᴛʀᴀɴꜱʟᴀᴛᴇ ᴛʜᴇ ꜱʏᴍʙᴏʟɪᴄ ʟᴏɢɪᴄ ɪɴᴛᴏ ᴘʀᴏᴘᴏꜱɪᴛɪᴏɴᴀʟ ʟᴏɢɪᴄ.
₂₅. ɢ → ᴅ ∧ ᴋ
₂₆. ᴅ → ~ɢ
₂₇. ~(ɢ ∧ ᴅ) → ᴋ
₂₈. ɢ ∨ ᴋ → ~ᴅ
₂₉.~ᴋ ∨ ᴅ → ~ɢ
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