document.write( "Question 680763: Can anyone help me solve this problem for Logic? (P → Q) ↔ (星 ∨ Q)?
\n" ); document.write( "There are no premises given. Just that which is the goal id really appreciate it. \n" ); document.write( "
Algebra.Com's Answer #422459 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We'll do each case separately then we'll\r\n" );
document.write( "put the four cases into a truth table:\r\n" );
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document.write( "(P → Q) ↔ (星 ∨ Q)\r\n" );
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document.write( "Let \"T\" mean \"true\" and let \"F\" be \"false:\r\n" );
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document.write( "Case 1:  P is true and Q is true:\r\n" );
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document.write( "(P → Q) ↔ (星 ∨ Q)\r\n" );
document.write( "(T → T) ↔ (曷 ∨ T)\r\n" );
document.write( "   T    ↔ ( F ∨ T)\r\n" );
document.write( "   T    ↔     T\r\n" );
document.write( "        T\r\n" );
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document.write( "Case 2:  P is true and Q is false:\r\n" );
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document.write( "(P → Q) ↔ (星 ∨ Q)\r\n" );
document.write( "(T → F) ↔ (曷 ∨ F)\r\n" );
document.write( "   F    ↔ ( F ∨ F)\r\n" );
document.write( "   F    ↔     F\r\n" );
document.write( "        T\r\n" );
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document.write( "Case 3:  P is false and Q is true:\r\n" );
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document.write( "(P → Q) ↔ (星 ∨ Q)\r\n" );
document.write( "(F → T) ↔ (政 ∨ T)\r\n" );
document.write( "   T    ↔ ( T ∨ T)\r\n" );
document.write( "   T    ↔     T\r\n" );
document.write( "        T  \r\n" );
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document.write( "Case 4:  P is false and Q is false:\r\n" );
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document.write( "(P → Q) ↔ (星 ∨ Q)\r\n" );
document.write( "(F → F) ↔ (政 ∨ F)\r\n" );
document.write( "   T    ↔ ( T ∨ F)\r\n" );
document.write( "   T    ↔     T\r\n" );
document.write( "        T  \r\n" );
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document.write( "It is true in all four cases, so it is a tautology.\r\n" );
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document.write( "Or you can do it as a truth table which is equivalent to\r\n" );
document.write( "the four cases above:\r\n" );
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document.write( "        | P | Q | 星 | P → Q | 星 ∨ Q | (P → Q) ↔ (星 ∨ Q |\r\n" );
document.write( "case 1: | T | T |  F |   T   |    T   |         T          | \r\n" );
document.write( "case 2: | T | F |  F |   F   |    F   |         T          |  \r\n" );
document.write( "case 3: | F | T |  T |   T   |    T   |         T          |  \r\n" );
document.write( "case 4: | F | F |  T |   T   |    T   |         T          |    \r\n" );
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document.write( "Since the last column came out all trues, the original statement\r\n" );
document.write( "is a tautology.\r\n" );
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document.write( "Edwin
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