**Core Concept**
The question is testing the ability to identify a molecular diagnostic test for an autosomal recessive disease characterized by dysfunction of mucus-secreting cells, such as cystic fibrosis. This disease is caused by mutations in the CFTR gene, which encodes a chloride channel responsible for regulating the thickness of mucus.

**Why the Correct Answer is Right**
To determine if the woman and her husband are carriers of the disease, a test that can detect mutations in the CFTR gene is required. PCR (Polymerase Chain Reaction) and sequencing are molecular techniques that can amplify and sequence the CFTR gene, allowing for the detection of mutations. PCR amplifies specific DNA segments, and sequencing determines the order of nucleotides in the amplified DNA. This combination of techniques can identify mutations in the CFTR gene, making it a suitable test for detecting carriers of the disease.

**Why Each Wrong Option is Incorrect**
**Option A:** Northern blot is a technique used to detect specific RNA molecules, but it is not suitable for detecting mutations in the CFTR gene. Northern blotting is typically used to study gene expression levels, not to identify specific mutations.
**Option C:** Southern blot is a technique used to detect specific DNA sequences, but it is not as sensitive as PCR and sequencing for detecting mutations in the CFTR gene. Southern blotting can detect large-scale deletions or rearrangements, but it is not suitable for identifying point mutations.
**Option D:** Western blot is a technique used to detect specific proteins, but it is not suitable for detecting mutations in the CFTR gene. Western blotting can detect protein expression levels, but it does not provide information about the underlying genetic mutations.

**Clinical Pearl / High-Yield Fact**
When testing for genetic disorders, it's essential to choose a diagnostic test that can detect the specific mutation or mutations responsible for the disease. In the case of cystic fibrosis, PCR and sequencing are the most suitable tests for detecting carriers of the disease.

**✓ Correct Answer: B. PCR and sequencing**