Given the facts (i–iv) about the World Cup, evaluate the statements using truth conditions and the truth tables of connectors to find the ‘false’ statement(s).
(i) Argentina has won the World Cup twice: 1978, 1986
(ii) Germany has won it four times: 1954, 1974, 1990, 2014
(iii) France has won it twice: 1998, 2018
(iv) Japan has never won it
(i) Argentina has won the World Cup twice: 1978, 1986
(ii) Germany has won it four times: 1954, 1974, 1990, 2014
(iii) France has won it twice: 1998, 2018
(iv) Japan has never won it
Show Hint
- If [Argentina won the World Cup in 1986] then [Germany won it in 1998].
- [Germany didn’t win the World Cup in 1986] and [France won it in 1990].
- [Argentina didn’t win the World Cup in 1986] or [Japan has never won the World Cup].
- If [Argentina didn’t win the World Cup in 1978] then [France won it in 1990].
The Correct Option is A, B
Solution and Explanation
Argentina did win the World Cup in 1986, so the antecedent is true. Germany did not win the World Cup in 1998; France did. Hence, the consequent is false. A true antecedent with a false consequent makes the conditional false.
Step 2: Evaluating option (B).
Germany did not win the World Cup in 1986, which is true. France did not win the World Cup in 1990; Germany did. Hence, the second conjunct is false. A conjunction with one false part is false.
Step 3: Evaluating option (C).
Argentina did win the World Cup in 1986, so the first disjunct is false. Japan has never won the World Cup, so the second disjunct is true. A disjunction with at least one true part is true.
Step 4: Evaluating option (D).
Argentina did win the World Cup in 1978, so the antecedent is false. A conditional with a false antecedent is true regardless of the consequent.
Step 5: Conclusion.
Only options (A) and (B) are false.
Final Answer: (A) and (B)
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