Logical Reasoning, Sentence Logic

Tautologies, Contingencies, Contradictions

 

  1. If you know that “neither Canada nor Britain will support the proposal,” what do you know about the following?
    1. Canada will not support the proposal.
    2. Canada will not support the proposal or Britain will not support the proposal.
    3. It is not the case that if Canada does not support the proposal, then Britain will support the proposal.
    4. Canada will not support the proposal and Britain will not support the proposal.

 

  1. If you know that “if Carol attends the party, then John will not attend,” what do you know about the following?
    1. Either Carol attends or John does not attend the party.
    2. Either Carol does not attend or John does not attend the party.
    3. If John attends the party, then Carol does not attend the party.
    4. If John attends the party, then Carol will leave early.

 

  1. If you know that “it is not the case that both Carol and John attend the party,” what do you know about the following?
    1. Neither Carol nor John attends the party.
    2. Carol does not attend the party.
    3. John does not attend the party.
    4. If Carol attends, then John attends the party.
    5. If Carol attends, then John does not attend the party.

 

  1. If you know that “interest rates will rise if bonds go down,” what do you know about the following?
    1. If interest rates do not rise, then bonds will not go down.
    2. If bonds do not go down, interest rates will not rise.
    3. Bonds will go down if and only if interest rates will rise.
    4. Either bonds do not go down or interest rates do not rise.

 

  1. If you know that “If either Canada or Mexico approves the plan, then both Guatemala and Honduras will not benefit,” what do you know about the following?
    1. If either Canada or Mexico approves the plan, then Guatemala will not benefit.
    2. If either Guatemala or Honduras will benefit, then neither Canada nor Mexico approves the plan.
    3. It is not the case that neither Canada nor Mexico approves the plan or Guatemala and Honduras will benefit.
    4. If Canada approves the plan, Honduras will benefit.